How can Jesus ‘not know’ the time of the Final Hour?
But of that day or hour no man knoweth, neither the angels in heaven, nor the Son, but the Father. (Mark 13:32). Matthew leave out “Son”, but adds “only” to Father, producing seemingly the same result.
Fr. Hugh Barbour O. Praem writes on Catholic Answers states: We need to remember that the word to know in the Semitic senses used in Scripture is very diverse and rich and does not refer only to mental information but to actions and offices. Thus we will argue that Jesus “did not know” only in the sense of “not having been sent to reveal”- it is not his office or his Mission to reveal the “times and the dates which the Father has fixed by his own authority” (Acts).
This the hour, in fact it is Jesus’ own coming. Is Jesus really saying that he doesn’t know his own Hour?: “Then the sign of the Son of Man will appear in heaven, and then all the tribes of the earth will mourn, and they will see ‘the Son of Man coming on the clouds of heaven’ with power and great glory. And he will send out his angels with a loud trumpet call, and they will gather his elect from the four winds, from one end of heaven to the other.” (Matt 24:30:31)

It may come as a surprise to many to learn that this claim (that, in his humanity, Jesus did not know the day and the hour of the Final Judgment) has been condemned by several popes as a heresy. In fact, it would be impossible to hold this view without implicitly maintaining either the heresy of Nestorius (dividing Christ into two persons, one human and the other divine) or of Arius (denying the divinity of Christ all together).

The specific heresy which claims that Jesus did not know the exact time of his second coming is called Agnoeticism – Fr. John Hardon defined the Agnoetes (those who held this heresy) as follows, “A sect of Monophysites who held that Christ was subject to positive ignorance. The leading exponent of its error was Deacon Themistios of Alexandria. He was condemned by the Church, which declared that Christ’s humanity cannot be ignorant of anything of the past or of the future. To attribute ignorance to Christ’s human nature is to profess Nestorianism (Denzinger 474-76).” (Modern Catholic Dictionary, “Agnoetes”)

As God, it is most certain that Christ knew and knows all things. However, what the heretics claimed was that the Lord was ignorant in his humanity, in his human intellect. From Ludwig Ott’s Fundamentals of Catholic Dogma:

“Christ calls Himself the Word become Man, the Light of the World (John 8,12), which is come into the world, in order to bring the true knowledge to mankind (John 12,46); He calls Himself the Truth (John 14,6), and gives as the purpose of His coming into the world the giving of testimony to the truth (John 18,37); He permits Himself to be called Teacher (John 13,13). He is, as Holy Writ witnesses, full of grace and truth (John 1,14), full of wisdom (Luke 2,40); in Him are all treasures of wisdom and knowledge hidden (Col. 2,3). He knows about happenings which occur far away (John 1,48; 4,50; 11,14), and sees through the heart of man (John 1,47; 2,24 et seq.; 4,16 et seq.; 6,71). With this is irreconcilable the notion that Christ’s human knowledge is defective or erroneous.” (Book III, Part I, section 2, chapter I – 23.4)

Magisterial texts on the perfection of Christ’s human knowledge
“If anyone says that the one Jesus Christ who is both true Son of God and true Son of man did not know the future or the day of the Last Judgment and that he could know only as much as the divinity, dwelling in him as in another, revealed to him, anathema sit.” (Pope Vigilius, Constitutum I of 14 May 553)

The following proposition is condemned: “The natural meaning of the Gospel texts cannot be reconciled with what our theologians teach about the consciousness and the infallible knowledge of Jesus Christ.” (Pope Pius X, Lamentabili of 1907)

The following proposition is rejected: “The opinion cannot be declared certain, which holds that the soul of Christ was ignorant of nothing but from the beginning knew in the Word everything, past, present and future, that is to say everything which God knows with the ‘knowledge of vision’.” (Pope Benedict XV, Decree of the Holy Office of 1918)

The following proposition is rejected: “The recent opinion of some about the limited knowledge of the soul of Christ is not to be less favoured in Catholic schools than the ancient opinion about his universal knowledge.” (Pope Benedict XV, Decree of the Holy Office of 1918)

From these texts we learn that, even in his human intellect and soul, Christ Jesus knew – with an “unlimited,” “universal,” and “infallible” knowledge – “everything, past, present and future.” Specifically, the Lord knew “the day of the Last Judgment.” As God, Christ most certainly knew and knows all things without any qualification whatsoever. And, even as man, we affirm that our Savior knew and knows all things.

St. Augustine offers the following commentary: “According to the form of God everything that the Father has belongs to the Son for All things that are mine are yours, and yours are mine. According to the form of a slave, however, his teaching is not his own but of the One who sent him. Hence of that day or hour no one knows, neither the angels in heaven, nor the Son, but the Father only. He is ignorant of this in the special sense of making others ignorant. He did not know it in their presence in such a way as to be prepared to reveal it to them at that time.”

He is said not to know, says St. Augustine, what he will not make others know, or what he will not reveal to them. (Witham)

So too the Catechism: “Christ enjoyed in his human knowledge the fullness of understanding of the eternal plans he had come to reveal. What he admitted to not knowing in this area, he elsewhere declared himself not sent to reveal. (ref Acts 1:6,7) So when they had come together, they asked him, “Lord, is this the time when you will restore the kingdom to Israel?” 7 He replied, “It is not for you to know the times or periods that the Father has set by his own authority.”(CCC 474)

Pope St. Gregory the Great on the Son’s knowledge of the day and hour
“…how can one who professes that the Wisdom of God himself became incarnate ever maintain that there is anything which the Wisdom of God does not know? It is written: In the beginning was the Word and the Word was with God and the Word was God. […] All things were made through him (John 1:1,3). If all things, then undoubtedly the day and the hour also. Who would then be so foolish as to say that the Word of the Father made something he did not know? Scripture again says Jesus knowing that the Father had given all things into his hands… (John 13:3). If all things, then certainly the day and the hour also. Who then is so foolish as to say that the Son received in his hands what he was ignorant of?” (Pope Gregory the Great, Letter to Eulogius of 600)

A Jewish Wedding helps us to Understand
One of the little-known aspects of Jewish culture was the wedding ceremony. When a bride and groom were to be married, a celebration would ensue. It took time to prepare the meals, the water, the wine, as well as for people to make travel plans to attend the wedding. Of course, in order to prepare for such a celebration, people had to know what day the wedding would occur. The custom of the groom was to prepare a room-addition to the father’s house. This is where the new bride and groom would reside after the wedding. it was the custom that the father would then “officially” declares the room addition ready and give the son permission to go get his bride. Of course, the trumpeters were waiting for the official command by the father of the household for the son to go get the bride. It was customary to say that no one knew the day nor the hour when the father would send the son to get the bride. It was a sign of respect for the father. It was a cultural thing. So, when Jesus said that no one knows the day nor the hour, he was reflecting the cultural norm. It did not mean he did not actually know the day nor the hour.- from CARMS apologetics website
St Aquinas tackles it in Summa Theological III Q.10 Art.2: “He is said, therefore, not to know the day and the hour of the Judgment, for that He does not make it known, since, on being asked by the apostles (Acts 1:7), He was unwilling to reveal it; and, on the contrary, we read (Genesis 22:12): “Now I know that thou fearest God,” i.e. “Now I have made thee know.” But the Father is said to know, because He imparted this knowledge to the Son. Hence, by saying but the Father, we are given to understand that the Son knows, not merely in the Divine Nature, but also in the human, because, as Chrysostom argues (Hom. lxxviii in Matth.), if it is given to Christ as man to know how to judge—which is greater—much more is it given to Him to know the less, viz. the time of Judgment.”

The answer is difficult to comprehend, and even more so for the untrained reader. Even St Thomas I feel has struggled with this particular passage and seems to know it. His comparison to the verse from Genesis is quite brilliant, because he shows that although God knows that Abraham fears him, yet He says “now I know”.