They'll remain locked in the loop of "We ARE right, SO you're wrong" which they call logic.
That is how it works. They come from the standpoint that they are absolutely right - even when they are wrong, which of course they never are. Therefore, if you disagree, you must - by definition - be wrong. And if you are wrong, then there is no need to listen to your arguments because, even when you are right, you are actually wrong. "Wrongness" is thus defined not in absolute terms, but by comparison with that which is held to be right. QED.
This is why you can never win an argument with a believer, in the same way that you can never win an argument about the existence of God with a Jesuit. The only way out is to shoot them (or expell them).