What is the purpose and the meaning of the tree of Life?

I don't think it is explicitly stated that Adam and Eve are mortal before the fall, but why would there be a tree that makes them immortal if they weren't? And why are they allowed this tree (Gen 2:16), but not knowledge of good and evil? The implication being that eternal life is being Godlike in an acceptable way, but being knowledgeable of good and evil isn't.

I'm not very knowledgeable about the Bible, so you can correct me when my theory doesn't match the text.

My understanding was that God had created the angels, probably before he created the Earth. The angels had many of the same properties as God, so they knew good and evil and were immortal. At that time, Lucifer turned against God. The angels were immortal, so Lucifer was also immortal. God would be battling Lucifer for eternity. God didn't want to duplicate that with humans, so he didn't make humans immortal but allowed for them to be immortal by eating from the tree of life. When Adam and Eve ate from the tree of good and evil, they now had the possibility of turning into another Lucifer, so God took away their ability to become immortal by taking away their access to the tree of life.

I'm not sure how I'd answer that if I couldn't ask why God did something in any coherent fashion. I don't think I agree with your teacher that asking why God does something should be disallowed. If God is completely random with no coherence or logic, God would be not just incomprehensible but also unrelatable. God would be like an alien doing random actions for no reason whatsoever.

I do agree with your teacher at the edges where there are incomprehensible human issues. Why did God create free will? Why did God allow evil in the world? Those are questions that can't be answered by looking for God logic because those are the questions that are beyond comprehension. However, I think there must be some questions where people are allowed to ask why God did something or the Bible would be completely illogical.

Edit: I thought about this for a bit and think I can answer it from the writer's viewpoint also. I'm wondering if I'm misunderstanding your question.

From the writer's view, polytheism was prevalent at the time. The Bible was an attempt to push monotheism. The placement of angels in the story explained what was going on with the many gods and why there were good and bad gods, which they already believed in at that time. The garden story explained why humans didn't have the same powers as the gods. The creation part pushed the idea of one God above all the other angels (gods). The tree of life was written in to explain why humans die and gods don't.