Denial of evidence and reason
Confirmation bias:


  Confirmation bias, also called confirmatory bias or myside bias, is
  the tendency to search for, interpret, favor, and recall information
  in a way that confirms one's beliefs or hypotheses, while giving
  disproportionately less consideration to alternative possibilities.


A feature of this bias is belief perseverance:


  ... when beliefs persist after the evidence for them is shown to be false ...


Confirmation bias is an umbrella term for a variety of strategies and effects that may be applicable in different situations, including self-justification, self-verification, attitude polarization, escalation of commitment, cherry picking, etc, etc.  See the duplicate questions I listed in the comments above for more varieties of these.  You may find that some sub-category of confirmation bias is more apt to your question.

Note: Cognitive dissonance refers to the cause of a number of possible inconsistency reduction strategies, of which belief perseverance is one.

Note: Denial refers to an ego-defence mechanism - ie, it applies only if the person feels personally threatened by the inconsistency.