It's an issue of authority. If someone says that something is true, and you prove them wrong, you've made them look like a weak thinker or out of touch with reality. This can actually damage their relationships with the people around them. If the issue is actually important, you should go to them privately and give them the information in a manner that makes it clear that you are looking to help them instead of just calling them out. If the issue is not important, often (in context) their posturing of "I know better" is more important than actually being correct, so just let it slide.
Sometimes, it can also be a issue of identity (left/right politician, Java/Lisp programmer…)[1]. If you attack an idea that someone attached to his identity, it will be like you attack his very being. Common reactions can be dismay, denial, or even violence.
