"A man convinced against his will
Is of the same opinion, still." (Laurence J. Peter (Oh my, I love Google...))
Have you ever gotten in a discussion with someone, marshalled your arguments, been accurate, witty, overwhelmingly convincing... and have your "opponent" (if you will), continue to argue because he isn't interested in facts, he just wants to hold on to his opinion regardless of anything you, or anyone else has to say.
Of course, the other aspect of this is Galileo, for example, with his "eppour si mouve" or however that is appropriately spelled, when forced to recant the heliocentric view of the, well we'll call it, universe. He agreed with the authorities out loud, but inside, he knew that Copernicus had a few little problems.
But this is actually two sides of the same coin. Galileo's "Church Authorities" would not accept all the logic and fact and "convincing arguments" of Galileo, because it conflicted with their preconceived and prejudiced beliefs. So, what do you do, in the waning hours of the discussion, when it becomes obvious that the "other side" simply dismisses any arguments you have because he isn't really interested in the truth of the matter. He just likes to argue. Well, I guess that you just shake your head a bit, and walk away, knowing that invincible ignorance will defeat logic and reason every time. At least with some people.
Jerry. The Bottle Washer