Do all Christians (not just Catholics) believe in the idea of infallibility?
For Catholics, the Pope speaks infallibly in certain situations, though this is obviously rejected by Protestants. But both Catholics and Protestants agree on a different area of infallibility, which is the writers of Scripture. Quoting St. Paul (or any other writers of the Old or New Testament) as an authoritative source of truth necessarily implies that we believe the writers speak infallibly.
This is an interesting idea that I don't think is always acknowledged.