The opening post talks about "publicly making a mistake", which I think meant making a post or comment that turns out to be wrong. (It also talks about admitting your mistakes, which I agree does refer to "old mistaken beliefs".) I suggest that we should feel some measure of embarrassment for making a post or comment that turns out to be wrong, even if it feels like (or appears as if) we were being careful/not foolish when we wrote it. The latter standard is too loose and subjective, hence easily rationalized away.