David P. Redlawsk explains it:
The reality is that “facts” are unlikely to mean much to those who believe in their gut that Obama is not American. Political psychologists call this “motivated reasoning.” It goes something like this: I dislike someone; I learn something positive that should make me feel better about him; instead, I dislike him as much or even more. This is clearly irrational, but our feelings about people are complicated, and we tend to hold on to them even in the face of contradictory information. This is not unique to those who dislike Obama.
We are all somewhat impervious to new information, preferring the beliefs in which we are already invested. We often ignore new contradictory information, actively argue against it or discount its source, all in an effort to maintain existing evaluations. Reasoning away contradictions this way is psychologically easier than revising our feelings. In this sense, our emotions color how we perceive “facts.”
They do; and it's important always to keep this in mind. But there remains something called fact, rather than "fact", and empiricism is our only real recourse in public debate. That's why producing a birth certificate is dispositive. It should end the discussion. I might add that merely asking a presidential candidate to produce such a certificate does not seem illegitimate to me. It may be maddening or unfair. But that's the price of public life. And the sign of a mature politician is his or her ability to see that and allow the ethic of transparency trump the humiliation of exposure. Obama easily passed this test.