This is the result of cognitive dissonance. If a person believes one thing but the evidence suggests another thing the brain enters a position of "stop." We can't act without having some level of faith that our action is "correct" (or at least correct enough). The cognitive dissonance must be resolved before the brain can move forward.

There are three possible paths out of this dilemma:

1. Ignore the evidence. In this case the belief is held on to and we can move forward, unperturbed by the contraindicating evidence. All that is required to choose this path is the slightest doubt about the evidence, or the most brainwashed faith and trust in the belief and we can convince ourselves that it's OK, possibly even morally imperative to ignore the evidence.
2. Adjust the evidence to fit the belief: The belief is held on to, though the evidence is not in our brains in its original form. In this case however, the seed has been planted. If you only see the evidence once it is easy to keep the false belief. Thus the power of the Memory Hole. However, if the evidence keeps coming, this path out of cognitive dissonance requires ongoing effort and eventually leads to realization that the belief is wrong.
3. Allow your beliefs to change to fit the evidence. This is by far the most difficult path, and can be very painful if the belief is a core belief. We have been brainwashed to believe in "the authorities." We trust them. It is a core belief for many, trained since almost birth, i.e. Sesame Street and/or Preschool, both of which were created by the Carnegie/Rockefeller foundation.

For me personally, I have learned to let go of my beliefs. I hold onto them only tightly enough to act, but no tighter. I recognize that they can change at any point with new evidence (and cogitation on that evidence). If you know the Truth, you simply can't see evidence to the contrary. The only thing I know with absolute certainty, is that I know Jack Shit.