The Backfire Effect — why you can never win an argument online

"What should be evident from studies on the Backfire Effect is that 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."

Back (see what I did there?) story here.

David McRaney's in-depth treatment here.