1. You don’t know who wrote what if you weren’t in the room when it was written.
2. According to their own propaganda, even though the credits said Lennon/McCartney, they didn’t have a composing and songwriting collaboration - Lennon wrote some songs, McCartney others. The Lennon/McCartney was a convenience of publishing.
3. Neither of them could read music, and Lennon was an extremely mediocre musician. The change in the music after George Martin came on board is so huge that it obviously goes way beyond “arranging”.
4. The banality and mediocrity of their post Beatles music would lead a reasonable person with knowledge of music and the music business to question their capacity as composers.
Boy, are you touchy, lol!