One of the reasons that the Jews did not recognize that Jesus was the Messiah can be easily understood looking at this passage. A crowd of people had gathered around Jesus, asking him questions and listening to what he taught and replied. Here is the passage to look at:
So the crowd answered him, "We have heard from the law that the Messiah remains forever. Then how can you say that the Son of Man must be lifted up? Who is this Son of Man?" (John 12:34).
When the Jews say, "the law," they mean what is written in the Torah, in their scriptures, what Christians call the Old Testament. So they have the impression from some scripture that the Messiah will live forever, remaining with the people until the end of time. Where have they seen this written? Look to Psalm 89:4-5.
"I have made a covenant with my chosen one; I have sworn to David my servant: I will make your dynasty stand forever and establish your throne through all the ages" (Psalm 89:4-5).
This is one of the places in scripture where the Jews have the impression that the Messiah will be a man, a descendant of David, who will be just like David (a king with the throne of the Israelites), who will "stand forever." So you can understand that with these words of prophecy from God most Jews thought that another David, but this time one who rules on earth forever, was to be the Messiah. Thus they are confused and dismayed when Jesus says that he, the Son of Man, would have his time of death, and then resurrection into heaven. When Jesus calls himself the Son of Man, he is reminding people that he is indeed in a human form, that he is not just occupying a body, or an illusion of being one of mankind. The crowd gets that, but then figure that the Son of Man must be a different person than the expected Messiah.
This is one reason why the Jews did not recognize Jesus. They developed a certain mental image based on scripture (and done so in good faith), but then did not have sufficient trust of God that he can and will work marvels and deliver the Messiah in ways they cannot imagine, visualize, or comprehend.
Jesus tries to explain to them how this is by comparing himself to the light (not "a" light, but the light of God).
Jesus said to them, "The light will be among you only a little while. Walk while you have the light, so that darkness may not overcome you. Whoever walks in the dark does not know where he is going. While you have the light, believe in the light, so that you may become children of the light" (John 13:35-36).
Now, Jesus is not trying to confuse them or be obscure. He is with a few sentences giving them a lot to think about, knowing that there is not much time left for him, as he says this shortly before the Last Supper. So Jesus is leaving those in the crowd with a few powerful images to refute the stereotype expectations they had of what the Messiah would be like, and then left them to think about it. Some would have understood his words, looking back on them just a matter of days later when Jesus' death and resurrection unfolded. Others would never have understood.
What Jesus was saying is that yes, as Son of Man, he is there as a real human being, a member of the human race, but that as Son of God, he is also of God's light, and that light is of course eternal. Jesus is thus saying he is not at all in contradiction of the scripture, just, actually "above and beyond," so to speak, their expectations. They expected a Messiah who would be completely a human man, but one who would live and rule forever, and bring their faith to the entire world. Jesus is exactly that, but not one who is going to do so as a man living forever among humans.
You may wonder why God did not "opt" to, in fact, have Jesus do just that: to live as a human among humans forever. The answer is simple. The Messiah is needed to draw humans closer to God, not to provide a living intermediary that would, in fact, be an additional "layer" between God and humans. Jesus brought the face of God to humans but the intention is that humans have the New Covenant with God which brings them closer to God, an upward reaching toward God, rather than God sending a governor, for lack of a better world, to "rule," while God is more distant, rather than closer. This is why Jesus often explained that the Kingdom of God is at hand. By "at hand" Jesus meant both "now" but also "within reach." The Messiah makes God more, not less, accessible to humans.
The Jews, in all fairness, could not have easily imagined that this is what God planned. They would have needed a lot of faith to understand that God would fulfill the scriptures in a way that they simply had not expected. Like the square peg in the round hole, the Jews who disbelieved were continuing to walk around with their square or their circular image of the Messiah, and when they did not see a match they would move on looking for the next "Messiah candidate" (and there were plenty, though not a single one performed the miracles that were Jesus' alone as only he had God's authority).
So Jesus is explaining to them that yes, he is the descendant of David, and yes, he has the throne, from God, but that the "forever" of it is when Jesus returns to God in the light of his eternity, not as his bodily Son of Man form. Jesus is explaining that the light of God is there with them, for a short time, while Jesus lives and walks among them. While the light will go back to God, those who believe in Jesus and follow him completely will therefore still benefit from the light, even though the light has gone back to God, because they are now become "children of the light." Jesus as the light of God that God has sent does indeed return to heaven, and the light itself does not stay on earth, nor can any human claim to have it, but instead, those who believe and heed what Jesus taught about God's expectations, God's Kingdom and the New Covenant are "children of the light" and therefore know the way and are not in darkness. It's like when you have memorized your way through the rooms of your home and can walk through them even in the dark, just to use a broad analogy. You "know the way" even though you don't have the light on. The children of Jesus "know the way" even though the actual light of Jesus has returned to heaven, and thus the children of Jesus do not walk in darkness, as do those who never believed in the light that he is and brought. Thus even when the light has returned to God those who believe in Jesus retain the knowledge of how to find God and the way just as if the light were still there, even though it is not.
I hope you have found this helpful.