1) The two were writing songs individually as early as All My Loving, which Lennon called a Paul song.
2) John has said that the death of Brian Epstein was really the beginning of the end of the band, and the point where the other three started to grow resentful of Paul. Apparently, and according to John, Paul started to feel that he had a personal obligation to hold the band together, and started to take charge, lead it, and attempt to be a sort of "father" of it. John felt that Paul was doing so, not for the good of the band, but for personal reasons. To paraphrase a particular interview: "He would come around and say, 'right, let's make a record!' But Paul did this because he had written something like ten songs, and he was ready to record them. I would say, 'well, give me a couple of days, and I'll knock some songs off.'"
3) Lastly, Lennon has also said he didn't remember the exact point where they all started to drift apart, and said something like, "you don't really remember falling in love either, it just sort of happens."