Definition from thefreedictionary.com:
dis·so·nance (ds-nns): Lack of agreement, consistency, or harmony; conflict
I keep stumbling lately upon references to the intriguing theory of Cognitive Dissonance from social psychology. I am very curious whether I am a victim of that when it comes to my reactions and opinions. According to the theory of cognitive dissonance, humans feel an inherent need to reduce the dissonance arising from conflicting evidence as much as possible. For example, smokers, even though they very well know that smoking is bad for their health, they come up with all kinds of irrational explanations about why they do not need to quit smoking; in other words they rationalize smoking. Human beings seem to be better at rationalizing their beliefs, rather than being rational. It is good to keep this in mind next time you are trying to convince someone with what you might think are perfectly rational arguments. Ours and our interlocutors preconceived notions and biases probably make it easier to agree to disagree.
Scientists have been performing experiments that seem to verify the theory of cognitive dissonance. The theory makes it possible to explain otherwise completely irrational behavior in certain circumstances. Some examples are given by Jonah Lehrer here.