It is not that they are afraid of being convinced. They fear only to appear ridiculous or to prejudice by their embarrassment their hope of winning over some third person to their side.

Don't forget about the last part of the quote. In my opinion it could be there most important part. That is the reason to argue, because we want to show how ridiculous their arguments are to third parties.

And that's when you repeat that he's a criminal who rigged two presidencies through fraud and intimidation, and who according to the law belongs in a jail cell at this very moment.