Cognitive dissonance

Cognitive dissonance is stress or discomfort caused by simultaneously holding contradictory ideas.

A mother, who believes that her son is a good boy, learns that he has committed a serious crime;
An atheist, who believes that there is no design or purpose in biological life, faces arguments and evidence that support the existence of a designer;
A preacher, who thinks he is righteous, finds himself tempted to sin;

People respond to the uncomfortable feelings associated with cognitive dissonance in a number of ways, including:

Resolution: Identifying the source of the contradiction and adjusting one one or both of the contradicting beliefs to eliminate the contradiction;
Rationalization: Inventing faulty justifications in an effort to maintain both contradictory ideas as true;
Denial: Denying the existence of a contradiction where one exists

George Orwell famously discussed cognitive dissonance in his novel 1984, using the term doublethink.