Reincarnation? Why? What purpose does it serve?
There is an idea that repeated lives will make people better. The idea is people will learn relationship and spiritual lessons the more lives they live. The problem with this hypothesis, it relies on individuals learning lessons and remembering from one life to the next as if live experiences were linked to eternal souls.
Jesus said we are like seeds planted in a field. Some rise good and strong, bear fruit and some fail, and are burnt and destroyed. It is a simple one chance and you are gone.
Now if you add the idea of eternal spirits, with eternal torture, the step into a reincarnation alternative makes better sense. Jesus appears to be talking about a simple love relationship, where you heart springs to life, new birth, or not, at which point the story ends.
My spiritual experience is this jump into new life, is the hardest thing a person can do, and all resist it to their last breath, or finally take the plunge. In reality, once you truly reject the open door, I think there is nothing left, no matter how many times the journey is repeated. That is why the Lord does not in force reincarnation, it would make no difference to the outcome, it might actually make it worse, by hardened souls recruiting more rebellion against love and life.