Tangent ahead. There's the sort of folksy saying "Don't argue with an idiot, they'll bring you down to their level and beat you with experience" (often attributed to Mark Twain, so I'm leaving it anonymous), and I think that these sayings are trying to get at the same thing. When someone believes something wrong, it could literally be beacuse of any other wrong belief that they have. Trying to untangle that structure is intractible.
