I will admit that I have not done in-deph research, in the sense of reading books, about the doctrine of reincarnation, but I can muster up my best guess as to why many people believe in reincarnation. I live near a lot of forestation and over the years, the forests have changed. Trees have collapsed after having been struck by lightning, the water levels in the nearby river have gone up and down [depending on the rain fall], the river has widened beause of erosion, wild mushrooms grow on their own, birds feed on the berries and make their homes in some of the bigger trees, etc.
Nature has a way of transforming by itself. Just as the forest will change due to animal habitation, rain, human interaction and so forth, perhaps the human soul also evolves over time. If it is possible for environments with plant-like entities to change and evolve over the years, perhaps the human soul also changesd and adapts based on its circumstances.
A seed is not a tree, but it has the potential to become a tree. Likewise, a soul is not an enlightened being, but it has the potential to. Let me state in plain terms that I am not endorsing reincarnation; I do not believe in reincarnation. That was just my best guess playing as devil’s advocate.
There are certain philosophical ramifications that could go along with reincarnation, like the epistemology you would have as a believer in reincarnation. If a truth is true now, does that mean that that truth can change or evolve over time, just as souls change? that’s a question I would ask a buddhist or a hindu (both of which believe in reincarnation). If it is so that truth changes, was there a point in time where reincarnation was not true? Is reincarnation something that became true? is it an eternal truth or did mankind come to learn about it? so on and so forth.