Pete has often asked what the real reason was for his firing out of the number which have been proposed. I think the most salient reason is George Martin's comment that Pete wasn't a good enough drummer. That is really what killed him.
Consider this, the Beatles were desparate for a recording contract and everyone else prior had turned them down. This seemed like the last chance for them. Although Martin said it wasn't a problem in that he could sub Pete with a session drummer, I'm sure the Beatles had other thoughts.
First of all, they were a live concert band at the time. If Pete couldn't back them on studio recordings, then how would he faithfully rendition their songs live? They couldn't use the session drummer live just so they could get the tune right. Bottom line, the B's wanted their drummer to be a credible presence both live and in the studio. This is truly the most compelling reason for Pete's canning.
Pete couldn't play "Love me do." Listen to the Anthology recording. He struggled with that. He couldn't find the beat and tried to play the accenting of it instead. It just didn't work. It felt too forced and stilted. I speak from my own experience as a drummer in my younger days. For a guy who's used to 4 to the floor, "Love me do" was confusing and challenging. Pete needed a simple soft back beat. He'd should have pulled out his brushes. He might have made it. If he had, who knows how much longer he could have lasted with them?
They were other challenging tunes ahead. Could Pete have provided the excellent backing that Ringo did for "Please please me?" The Beatles catalogue was not simply straightforward rock and roll. It was really a mix of the past and present styles of music. You'd have to have been a really versatile drummer to successfully complement the Beatles' wide range of musical diversity.
As far as Pete goes, all I can say is "Let it be, yeah, let it be, whisper words of wisdom, let it be."