I clipped this set of paragraphs from an article, and now, for the life of me, I can't remember the source publication. Saved them because I thought they illuminated quite well the reason why people don't change their minds, no matter how compelling or well-reasoned your argument might be.

...prejudice stems from a deeper psychological need and it is associated with a particular way of thinking. People who aren't comfortable with ambiguity and want to make quick and firm decisions are also prone to making generalizations about others. People who are prejudiced feel a much stronger need to make quick and firm judgments and decisions in order to reduce ambiguity.

And, they [the authors of the study] argue, it's virtually impossible to change this basic way that people think.

"Of course, everyone has to make decisions, but some people really hate uncertainty and therefore quickly rely on the most obvious information, often the first information they come across, to reduce it" says co-author Arne Roets of Ghent University in Belgium.

That's also why they favor authorities and social norms which make it easier to make decisions. Then, once they've made up their mind, they stick to it. "If you provide information that contradicts their decision, they just ignore it."