Here is an excerpt from The Atlantic by Lane Wallace, which shows why people cling to irrational beliefs even after proofs existing to the contrary:
“Why do people cling to an opinion even after they are presented with contradictory evidence?” said Lane Wallace. “The easy answer, of course, is simply that people are irrational.” But the way in which they are irrational is telling. In a new study, social science researchers have found that people employ “motivated reasoning to fend off any evidence that their strongly held beliefs are wrong. Many people feel that they are their opinions, and hate to lose arguments; as Vince Lombardi once said, “Every time you lose, you die a little.” So when confronted with new, troubling information, ideologues selectively interpret the facts or use “contorted logic” to make conflicting evidence just go away. In the study, even when presented with “compelling, factual data” from a trusted source, many subjects “still found ways to dismiss it. ” In fact, researchers found that exposing people to contradictory information actually “intensified” their existing beliefs, making them more rigid and entrenched. Needless to say, the findings do not offer much hope of “changing anyone else’s mind with facts or rational discussion.”