Of all the things we hate, is someone who will never admit they're wrong.
We know the kind of person - no matter what kind of facts you put you, they will never change. But, in a certain way, that turns out to be human nature. And indeed, one of the tenets of Dale Carnegie is: "A man convinced against his will, is of the same opinion still".
However what makes not admitting you're wrong, is blaming your wrongness on another person.
Always be quick to admit you are wrong and move on. It turns out that it will make you a so much better person!