I believe there are some subjects where people just (feel) one way or another and there is nothing anyone can say, do, or show them that is going to change their mind.
They view changing one's mind as being a weakness. In fact their ego is more concerned with "winning" than seeking the truth. If they change their mind and agree with you it's the equivalent of saying you're smarter than they are on this topic.
They simply cannot allow you that satisfaction.