Reincarnation is a common view in certain religious systems and spiritual paths. But some serious problems with it are never mentioned.

The basis of reincarnation is having a fixed number of souls, implying a fixed number of bodies. If you think humans can only reincarnate as another human, this means a fixed number of human bodies.

Maybe souls can be created to make up the difference, but then you will have too many of them making the problem worse, since souls live forever.

Assuming only human to human reincarnation: with the rapid population increase in the last few centuries, where did all the souls come from? And when massive civilization collapse occurs when fossil fuels run out, where will all these souls go as the human population suddenly decreases to perhaps 500 million?

So then you have to claim there are many worlds having humans and that the human souls are shared between these. That means that on one world there is population growth while on another there is decline. Who is micromanaging all this to ensure the accounting works out?

Then they say, "I'm an old soul" because they like antique furniture. But this furniture was constructed by the previous generation, so actually, they are a young soul. An old soul would like basket weaving and pottery and animal skins.