More likely Fermat was just mistaken. There have been numerous flawed proofs over the years --- most likely Fermat stumbled on one of those, realized the error

More likely Fermat was just mistaken. There have been numerous flawed proofs over the years --- most likely Fermat stumbled on one of those, realized the error (hence, never published), but never bothered to correct the note he'd left in the margins on of one his books.