1. "The existence of dissonance (or inconsistency), being psychologically uncomfortable, will motivate the person to try to reduce the dissonance and achieve consonance (or consistency)"
2. "When dissonance is present, in addition to trying to reduce it, the person will actively avoid situations and information which would likely increase the dissonance"
When you point out information indicating that a believer is wrong (or inconsistent) they feel uncomfortable (dissonance). To reduce that feeling, a common human reaction, they will automatically dismiss that information and often not even recognize that information as having anything to do with their mistaken belief. This reaction is strongly reinforced when they belong to a group which holds the same beliefs. No one wants to be wrong and therefor we tend to be blind to facts which do not conform to our beliefs. Science is a great way to neutralize this effect. We must be very careful however, since there have been many pseudo sciences developed by the persistency of the Cognitive Dissonance effect, they can however be distinguished by using the proper established scientific method:
"a method or procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses." “Another basic expectation is to document, archive, and share all data and methodology so they are available for careful scrutiny by other scientists, giving them the opportunity to verify the results by attempting to reproduce them.” (Wikipedia)
We can now understand why it is so hard or impossible to have a believer change their mind and why some unbelievers still believe in ESP or UFOs.