Pete, his drumming was not good. He couldn't hold time. Very inconsistent rhythm. I guess there also were some personality differences. As someone who suffers from depression, I feel great empathy for the struggles Pete went through, as he purportedly tried to commit suicide at some point. I'm glad he was able to get some help, and eventually through the Anthology recordings, he was able to receive some manner of monetary compensation.
But the brutal truth, the Beatles do not get to where they went without a far more competent drummer behind them. Still, how they "fired" him was pretty crummy.