In Matthew 24:36 and Mark 13:32, Jesus confesses to not knowing the day and the hour of His return, saying:
Mark 13:32-33
32 But of that day and that hour knoweth no man, no, not the angels which are in heaven, neither the Son, but the Father.
33 Take ye heed, watch and pray: for ye know not when the time is.
Here, in context, "know" means "have knowledge of" (see Matthew 24:42-51, Mark 13:33-37). Therefore, Jesus was not omniscient, as He lacked knowledge of something that God knew, as He states in the passage. And, in the account in Matthew, He specifically says that "only" the Father knew the information, in distinction from Himself.
However, if Jesus was fully God, then He did know the day and the hour. There is only one Person speaking in these passages - Jesus Christ. If Jesus Christ, allegedly fully human and fully divine, knew this information in any part of Himself, then the statement would simply be false, as He certainly did know it, even if He was refusing to call it to mind, or not sharing it with His "human side", etc.
Therefore, this passage is demonstrative of the fact that Jesus is not God, and has long been appealed to by Unitarians for that reason. Classical commentators, seeing this issue, exerted much effort attempting to prove that Jesus actually did know the day and the hour, but was essentially only stating that He would not declare it. This relies on equivocating on the meaning of "know", when as already stated, it clearly in context means "have knowledge of", and not "declare". In modern times, it is much more common to acknowledge that when Jesus said He did not know, He really did not have access to that knowledge at that point in time, appealing to modern Kenosis theories, which are not a part of the historical Trinitarian tradition, as they actually terminate in Jesus not being God, as described above.
What follows are some published Unitarian arguments dealing with the topic of Jesus not knowing the day and the hour, spanning from the 18th century to modern times.
The Doctrine of the Trinity, by Anthony Buzzard and Charles Hunting - Chapter 11, pg. 288
(Mark 13:32) This verse reports Jesus' statement that he did not know the day of his return. It seems plainly contradictory to assert that omniscient Deity can be ignorant in any respect. Some Trinitarians appeal to the doctrine of the divine and human natures in Jesus to solve the problem. The Son did in fact know, but as a human being he did not. This seems little different from saying that one is poor because one has no money in one pocket, though in the other pocket one has a million dollars. In this text it is the Son as distinct from the Father who did not know. It is therefore quite impossible to plead that only the human nature in Jesus was ignorant. The Bible anyway does not distinguish "natures" in Jesus as Son of God and Son of Man. Both are Messianic titles for the one person. If a witness in a court of law were to be asked whether he had seen the defendant on a certain day and he replies in the negative, meaning that he had not seen him with his defective eye, though he did with his sound eye, we would consider him dishonest. When Jesus referred to himself as the Son, he could not have meant a part of himself. The theory by which Jesus did and did not know the day of his future coming would render all of his sayings unintelligible. The plain fact is that a confession of ignorance is incompatible with the theory of the absolute Deity of Jesus.
Divine Truth Or Human Tradition, by Patrick Navas - Chapter 2
(Matthew 24:36) For the purpose of this examination, the key phrase is "nor the Son." According to the Gospel of Matthew (and Mark 13:32), even Jesus Christ, the Son of God, does not know (or did not know at that particular time) the day and hour of his future arrival. However, speaking with reference to the Father and Son, Trinitarian and professor of systematic theology Donald Macleod surprisingly claimed: "They share, too, the same glory. The Son's glory is a glory with the Father (John 17:5). The same is true of divine knowledge. Whatever the Father knows, the Spirit and the Son also know."
In light of Jesus' forthright admission that he did not know the day or hour of his return, it is unclear why some theologians feel compelled to propose theological propositions that the Bible does not speak of, and that, in fact, directly contradict what the Bible does speak of in a specific way. Of course it is not entirely true that whatever the Father knows the Son knows, as Jesus himself made clear; and yet this is a fact made evident elsewhere in Scripture.
In the opening of the book of Revelation, the apostle John spoke about what he had seen and heard as the "revelation of Jesus Christ, which God gave to him, to show his servants what must happen soon" (Revelation 1:1). This shows that the things revealed to John by Jesus Christ were according to the revelation given to Jesus Christ by God, which must imply - logically speaking - the "revealing" of knowledge that Jesus Christ did not previously possess, or else there would have been no need or occasion for God to have revealed it to him.
One God, Three Persons, Four Views, Edited by C.A. McIntosh - Section I.4 (Dale Tuggy)
Fact 15: Unqualified implications of the Son's limits
Clear NT texts imply that Jesus is less than God in respect of power, knowledge, goodness, authority, immortality, impeccability, and greatness. More precisely, these texts imply that Jesus lacked essential omnipotence (Mark 10:37-40; John 5:19-20, 30), essential omniscience (Matt 24:36; Mark 5:30-32; 9:21; 13:32; Heb 5:8), underived moral goodness (Mark 10:18), underived authority, essential untemptability, and essential immortality, as well as the divine attribute of being greater than all others (John 10:29; 14:28) - all of which are plausibly features that the absolutely perfect being must have.
Any competent writer would know, in authoring such texts, that they would lead the reader to think that God (a.k.a. the Father) is greater than Jesus and that Jesus is lesser than God in each of these respects. Thus, such a writer, if they believed that Jesus was as divine as is the Father, would warn the reader not to draw any such conclusions, or at least would offer some distinction intended to show that no such conclusions follow (e.g., that Jesus lacks essential omniscience "with respect to his human nature" only).
But these authors issue no such warnings or qualifications, in effect contrasting Jesus with God in these eight respects. If (the Trinitarian hypothesis) were true this would be very surprising. But it is expected, or at least not at all surprising given (the Unitarian hypothesis). Thus these facts too strongly confirm (the Unitarian hypothesis) over (the Trinitarian hypothesis).
Is Jesus Human and Not Divine?, by Dale Tuggy and Christopher Date - Section 1.8
1.8 Contradictions Implied by Jesus Having Both Divine and Human Natures
That they are not taught in Scripture is enough for a Protestant to set aside two-natures theories about Jesus. But such theories also bristle with conceptual problems. Like other unsuccessful speculations, they create at least as many problems as they're supposed to solve. These theories make Jesus into an impossible object, something which in principle cannot exist, like a square triangle. Here are four contradictions generated by this theory that Christ has both divine and human nature, when considered together with the Bible and Christian theology.
First, God is, as fully divine, supposed to be essentially omniscient, but Jesus explicitly said that the Father knew something that Jesus did not, thereby showing himself not to be essentially omniscient (Matthew 24:36; Mark 13:32). (One who is essentially omniscient can't at any moment of his existence fail to know some truth.) But no one can be and not be essentially omniscient.
Omniscience - The Attribute of the Father Only, by Joseph Hutton (1790-1860 AD), pg. 17-18
Our Lord's assertion is, that he knew not the day and hour. Shall we then suppose him to mean, that though he did know it as the Deity, he did not know it as a man; or, in other words, that the particular portion of his nature which was human, was not the source of his knowledge? What is this but to ascribe to our blessed master words which, if explained by him, would have been found to contain nothing better, even upon the Trinitarian hypothesis, than a flat and unprofitable truism; and which, unexplained, could be regarded in no other light than as a mere equivocation. Let it be remembered, as a fair and legitimate, though I must think it will appear a startling consequence of this mode of interpretation, that our Lord might, consistently with his character and with truth, have denied in one place, in terms as strong and direct as he affirmed in another, - saying I know, one moment, and I know not, as confidently the next, - his knowledge of the human heart, of the circumstances of his own approaching death, of the destruction of Jerusalem, of the general resurrection and judgment, in short of every thing which, as a mere man, he could not have known. Those whose minds revolt against such a theory and such a consequence, and who would not put an equivocation into the mouth of him who was "the truth," as well as "the way and the life," will probably agree with me, that Jesus would not have professed himself ignorant of that which he really knew, in any character or nature whatsoever, whether human or divine.
To suppose that the man, Christ Jesus, could, with truth and sincerity deny, what Jesus, the Divine Being, might, at the same time, have truly and sincerely affirmed, is certainly to suppose that the two natures were perfectly distinct; that there were subjects on which they did not communicate; and on which, therefore, the same mind was not employed to register their thoughts. It is to say, in short, that the words and actions of Jesus did not always flow from the same internal source; that though apparently, he was not really, one being, but that his outward and visible form was possessed and governed by two distinct regulating minds of opposite and inconsistent attributes. I think I may safely affirm that, amidst the multitude of opposing sects, there is not one that will pretend to maintain, upon scriptural grounds, such a doctrine as this.
A Statement of Reasons For Not Believing the Doctrines of Trinitarians, by Andrews Norton (1786-1853 AD) - Section II, pg. 60-61
According to those who maintain the doctrine of the two natures in Christ, Christ speaks of himself, and is spoken of by his Apostles, sometimes as a man, sometimes as God, and sometimes as both God and man. He speaks, and is spoken of, under these different characters indiscriminately, without any explanation, and without its being anywhere declared that he existed in these different conditions of being. He prays to that being whom he himself was. He declares himself to be ignorant of what (being God) he knew, and unable to perform what (being God) he could perform. He affirms that he could do nothing of himself, or by his own power, though he was omnipotent. He, being God, prays for the glory which he had with God, and declares that another is greater than himself. (See John 17, Mark 13:32, John 5:30, 14:28)
On the Doctrine of Two Natures in Jesus Christ, by Alvin Lamson (1792-1864 AD), pg. 17-20
Our next objection is of a graver character. The doctrine we are examining, implicates, as we conceive, the moral character of our Saviour, impeaches his veracity, and attributes to him deceit, equivocation, and falsehood. This is a very weighty charge. We cannot endure to hear the name of Jesus, even by supposition, coupled with fraud and dishonesty. We regard him as "holy, harmless, and undefiled," in a sense in which no other being who has ever trodden our earth, has a claim to be called such. The purity of his mind could not be surpassed; it was entire and perfect, partaking of the brightness of divinity. An inflexible love of truth, an openness, and beautiful and majestic simplicity, were among the most striking features of his character. For these features, for his purity, his ingenuousness, and his truth, we reverence him, and would combat with our whole strength whatever views tend to impair or destroy this reverence. We hold a belief of his integrity among our firmest, fondest persuasions, and this belief nothing would tempt us to resign. To be compelled to abandon it, to have our confidence in the pure character of Jesus of Nazareth shaken, and be forced to conclude, that in imparting his doctrines to the world, and even in his hours of familiar intercourse with his disciples, he made use of deceit, or mental reservation, would cause us insupportable gloom and anguish. We object to the doctrine of the two natures, that it wrests from us this precious persuasion, - a persuasion of his entire sincerity and explicitness.
Let it not be said, that the doctrine is not chargeable with any such consequence. It is, according to every view we can take of it, justly chargeable with it. Thus we are told that Jesus sometimes spoke and acted in his human, and sometimes in his divine nature; that when he said, that he could of himself do nothing, he meant, that as man he could do nothing, although as God he could do all things; when he declared, that he knew not the day and hour of judgment, we are to understand by this declaration, that he was ignorant of it as man, although he knew it perfectly well as God. Now this, we affirm, is precisely what, in a fellow mortal, we should call, by the mildest term, equivocation. It is absolutely inconsistent with that openness and integrity which we are authorized, by the laws of social intercourse, to expect from each other. When one affirms that he does not know a thing, he means, if he is an honest man, that he does not know it in any way whatever. It is vain for him to allege, that he knows it only in a certain character, that he is ignorant of it as man; as if a priest should declare, that he is ignorant of a fact as man, though he knows it as confessor; or a person should affirm, that as a corporeal being, he is ignorant of what as an intelligent or spiritual being he knows well enough. This will not save him from the charge of equivocation or falsehood. Let us beware of ascribing to Christ conduct which would be thought disingenuous or immoral in a fellow mortal. If he did not deceive, if he made the ordinary use of language, he could not declare, that he was ignorant of what he knew in any manner whatever. It is a poor subterfuge to say, that he was ignorant of it in his human, though he knew it in his divine nature. No matter in what way he knew it; if he knew it in either nature, he knew it in a personal capacity, his person including both natures: that is, he knew it in an absolute sense; and could not then, with reason or truth, declare his ignorance of it. Would his disciples, or those who heard him, suspect him of any reservation, or of using equivocal language? Would they not suppose, that when he told them he did not know or could not do a thing, his words were to be understood in their ordinary sense? If they were used in any uncommon sense, which he took no care to point out, how can he be defended from the charge of having made a deceitful use of language?
If words have any fixed meaning, our Saviour expressly disclaims the possession of any attributes strictly and properly divine: as omnipotence - I can of my own self do nothing; supreme, infinite goodness - Why callest thou me good? there is none good but one, that is God; omniscience - Of that day and that hour knoweth no man, neither the Son, but the Father. This is plain language; there is no mystery or obscurity in it. The terms, I, me, self, as everyone knows, always denote an individual or person, and they include the whole of that person; they are not appropriated to any part or member of such person; they comprehend all which goes to constitute him what he is, viewed as an individual or whole. In this sense our Saviour must have used them, or he must have been guilty of manifest prevarication. To say that by self he meant only the inferior part of his nature, and intended to assert only, that this part was not truly divine, or did not possess, inherently and of itself, infinite power and knowledge, is to make him express himself, as no honest man, not bereft of his sober senses, ever did or ever would.
Scripture Proofs and Scriptural Illustrations of Unitarianism, by John Wilson (1802-1868 AD) - Chapter 2, Section 1, pg. 109-111
The opinion generally entertained by Trinitarian commentators is, that, when our Lord declared ignorance of the precise time of his coming, he spoke only in his human nature. This opinion is well known to be founded on the hypothesis, that Christ possesses two natures, - the one human and the other divine: the former including all the sinless properties of humanity; and the latter, everything essential to the nature and perfections of the Deity. But as neither prophet, nor apostle, nor evangelist, nor any inspired person whatever, not even Jesus Christ himself, announced that he was in possession of these two natures, we dare not take for granted the truth of this opinion, even supposing the words under consideration could be explained in consistency with it.
The assumption, however, we are bold to say, would not answer the purpose intended. The strict integrity of our Lord's character - the moral perfection that shone so conspicuously in his discourses and behavior - forbids our conceiving him to assert, without the least apparent hesitation, - without the slightest modification of his own language, that he did not know the exact time of that event of which he had been treating; while he was conscious - as on Trinitarian principles he must have been conscious - of being acquainted with the precise moment of the fulfillment of his prophecy. To attribute to the righteous Jesus such an assertion of ignorance, and such a consciousness of knowledge, is surely imputing to him conduct which it will be difficult to clear from the charge of culpability. But, in truth, no plausible reason can be assigned for supposing Christ to know perfectly the exact time of an event, while he disclaimed all knowledge of it; except that which arises from the necessity of the case; - a necessity created only by the mysteries and contradictions involved in the popular doctrine of the Trinity.
On this subject, the observations of Abauzit are worthy of being quoted: "Supposing that Jesus Christ be the Supreme God, he cannot say, that he knows not the day of judgment, as on this supposition he knows it in an infallible manner by his Divinity. He cannot say in a general manner and without any limitation, that this day is unknown to him, without violating truth. The language which they have made Jesus Christ employ, in supposing that he had present to his mind this imaginary distinction, resembles that which I might hold, when, interrogated by a judge concerning facts which are very well known to me, I should reply, that they were unknown to me, under pretense that my body had no knowledge of them. It is as if one asked me if I had seen such a person, I should answer, no; because when I saw him I had one of my eyes shut, and did not see him with that eye. It is as if when one should desire me to write upon some subject, I should reply that I was not able to write, because my mind could not hold a pen. There is nobody who does not see how absurd such a mode of speaking would be. There is no absurdity a man might not advance, if he were allowed to employ similar reservation. A man might say, that he neither eats nor drinks, because his mind properly does not eat or drink. He might say, that he does not think, that he has not an idea of any one thing, that he remembers nothing, that he cannot reason, - because all these operations do not belong to his body. One might say, in speaking of Jesus Christ, that he was not born, that he did not suffer, that he was not crucified, that he did not die, that he was not raised again, or ascended into heaven, - because all this is not true of him with regard to his Divinity. One easily sees that this would be to institute an egregious abuse of language: one ought therefore to be cautious of attributing it to Jesus Christ, in supposing that he adopted this mode of expressing himself, in pretending that he declared to the world his ignorance of the day of judgment, because he knew it not as a man, though at the very time, as God, this day was perfectly known to him."
An Humble Inquiry Into the Scripture Account of Jesus Christ, By Thomas Emlyn (1633-1741 AD) - Section 2.2
(Why Two-Natures Speculations Don't Help)
What can be said against these clear arguments? I imagine our opponents have only one move left for evading them, and that is a distinction which serves them in all cases: they say Jesus Christ says these things about himself "as man only," while he had another nature "as God," which he reserved and excepted out of the case, so that when he says "I cannot do this myself," or "I am not to be called the chief good," or "I do not know this," etc., according to them, the meaning is: "I don't have these perfections in my human nature, nonetheless I know and can do all unassisted, and am the chief good in my divine nature, which also is more properly myself."
I intend now to expose the futility of this tricky move by showing how absurd it is to suppose that this distinction of two natures removes the force of such expressions from Christ's own mouth which in their natural and ordinary appearance proclaim his inferiority to God, even the Father. And I shall dwell more on this because it's the most popular and common evasion, and comes in at every turn, when all other relief fails.
It's reasonable for us to ask what hint of such a distinction of two natures they can point us to in any of these discourses of Christ. Should we devise or imagine for him such a strange and seemingly deceitful way of speaking simply to uphold our own precarious opinion? But I have several remarks to make about this common answer.
My first objection is that our blessed Lord Jesus Christ, if he was the supreme God in any nature of his own, he could not have said, it seems to me, consistently with truth and sincerity (which he always maintained strictly), that he could not do or did not know something which all this while he himself could do or did know very well - as surely as if he were the supreme God, he could and did. This would be to make him say what is most false and to equivocate in the most deceitful manner. Even if we should suppose he consisted of two infinitely distant natures, and so had two capacities of knowing and acting, yet since he includes them both, it follows that when he denies something of himself in absolute terms, without any limitation in the words or other obvious circumstances, he plainly implies a denial of its belonging to any part of his person, or any nature in it.
Although we may affirm a thing of a person which belongs only to a part of him, as I may properly say a man is wounded or hurt, though it only be in one part, suppose, an arm - yet I cannot rightly deny a thing of him which belongs only to one part, because it belongs not to another. I can't say a man is not wounded because although one arm is shot or wounded yet the other is unharmed. For instance, I have two organs of sight, two eyes. Now suppose I converse with a man with one eye shut and the other open. If being asked whether I saw him, I should dare to say that I didn't see him (without any qualification) meaning (to myself) that I didn't see him with the eye which was shut although I saw him well enough with the eye which was open, I fear I would be criticized as a liar and deceiver, notwithstanding such a mental reservation as some would attribute to the holy Jesus. For knowledge is the eye of the person; Jesus Christ is supposed to have two of these knowing capacities, the one weak, the other strong and piercing, discerning all things. Now as such a one, the disciples come to him and ask him when the end of the world and time of his coming shall be. He answers them by giving them some general account of the matter, but says that he didn't know the particular day and hour, nor did any know them except the Father, meaning (say my opponents) that it wasn't included in his human knowledge, although he knew it well enough with his divine nature, at the same time that he said absolutely and without qualification that the Son doesn't know it.
If Jesus Christ had a divine knowledge and nature, no doubt his disciples (who, if anyone, must have believed it) would have directed their question to that divine capacity of his rather than to the imperfect human capacity, and yet in answer to their question he says he didn't know the day, which would not be counted as sincere or truthful in ordinary people. But surely we mustn't think Jesus Christ was dishonest in this way, for in his mouth was no guile. Let us not impute it to him.