The beliefs we hold about the world affect how we see things, instead of the other way around. That is, we don't see things then believe. We believe first and then see. Our pet theories about other peoples motivations and preconceptions about what happened determine the kind of evidence you look for and the kind you reject. A basic tendency for people to favor information that confirms their existing beliefs.
It explains why two people can have a disagreement even though they are expose to the same evidence (attitude polarization) and how beliefs persist even in the face of contradictory evidence (belief perseverance). The problem arises when people recall information selectively and bias their conclusions.
This "phenomena" is called confirmation bias. It tests ideas in a one-sided way. If more people framed their arguments so they were more persuasive and neutral, and less resistant to opposisiton, more willing to be wrong, this kind of thing shouldn't happen as often. Being able to amicably disagree with people is a fantastic skill to have. I can see no greater intellectual benefit than the kind open communication brings from sharing your ideas in the face of respected adversity. As Aristotle once said:
"It is the mark of an educated mind to entertain a thought without accepting it."
