The backfire effect occurs when, in the face of contradictory evidence, established beliefs do not change but actually get stronger. The effect has been demonstrated experimentally in psychological tests, where subjects are given data that either reinforces or goes against their existing biases – and in most cases people can be shown to increase their confidence in their prior position regardless of contrary evidence.
What should be evident from the studies on the backfire effect is you can never win an argument online. When you start to pull out facts and figures, hyperlinks and quotes, you are actually making the opponent feel as though they are even more sure of their position than before you started the debate. As they match your fervor, the same thing happens in your skull. The backfire effect pushes both of you deeper into your original beliefs.
—You Are Not So Smart – The Backfire Effect