Douglas Harper's Etymology Dictionary
1968, "in a hierarchy, every employee tends to rise to his level of incompetence," named for (and by) Laurence Johnston Peter (1919-1990) Canadian-born U.S. educationalist and author, who described it in his book of the same name (1969).
Wikipedia
The Peter principle is a concept in management theory formulated by Laurence J. Peter and published in 1969 in which the selection of a candidate for a position is based on the candidate's performance in their current role, rather than on abilities relevant to the intended role. Thus, employees only stop being promoted once they can no longer perform effectively, and "managers rise to the level of their incompetence."
Usage examples of "peter principle".
Whenever she heard people talk about the Peter Principle, rising to your highest level of incompetence, she thought about her experience in field hockey.
Even John Mitchell -- whose reputation as a super-shrewd lawyer ran afoul of the Peter Principle just as soon as he became Nixon's first Attorney General -- lost his temper in an exchange with Sen.
He's a living example of the Peter Principle, and he's been passed over for promotion twice.