There is something very wrong with Peterson. I think it is because he has created a mental prison for himself that he cannot escape.
Peterson holds two different world views, and they argue with each other. Jung, on whom Peterson bases his world view is a transitory figure between Modernism and Postmodernism. Peterson believes the Modern idea of evolutionary biology effects behavior, yet also believe the Postmodern idea of stories and narratives control social behavior. I don't think he can reconcile these two different ideas. Jung's logic breaks down at a certain point, and one must believe him in an unscientific way.
There may be some other deeper conflicts in his behavior that we don't know about, such as his drug abuse, and what caused it. But even a non-intellectual can see he is deeply conflicted.