IMO this is one of the fringe benefits of a good math education. Almost everybody who does math for long enough, especially if you work in small groups with your peers, will have a moment of "oh, I see, I am totally wrong and you are totally right" and find out that being wrong does not make someone a bad person. And you will see your peers do the same.
It's one underrated side effect of clear and unambiguous reasoning. Yes, many things are grey areas, but there's value in a place where you can't throw up a muddle of goalpost-shifting and rhetorical tricks to run away from your own errors.