Exactly. They have very strong feelings that they are right, and won't be moved - not by arguments, research, evidence or anything else.

Just look at the guy telling me "they can't reason!". I asked whether they'd accept they are wrong if I provide a counter example, and they literally can't say yes. Their world view won't allow it. If I'm sure I'm right that no counter examples exist to my point, I'd gladly say "yes, a counter example would sway me".