He might have been unhappy about that, but if you believe his
biography, it was never his intention to leave.
But if he really did want to leave, it would have been because of
Ferguson's overall disapproval of Beckham's lifestyle off the
pitch. At most, the boot incident would be a final straw but not
the reason in itself.
The book did say something about the incident, but the newspaper
article I read back then didn't go into detail. Or maybe I can't
remember.