That's the title of a Scientific American article on cognitive dissonance and how best to handle people who refuse to believe the facts.
Experiments have shown that people will make up or distort things in order to reduce dissonance, which arises when a person holds two conflicting thoughts. Conflicting thoughts arise when someone lies, is dishonest, and such. If unchecked, it will continue in something like a feedback cycle.
Sounds like they are talking about President Park supporters. The article explains how lies or falsehoods cause people to justify themselves and lead to a distortion of reality. So, the worst thing to do is to tell pro-Park supporters that they are wrong. It will only cause them to reinforce their false beliefs and make them more radical.
They have been talking about cognitive dissonance for decades. I thought the best approach was to just observe people with cognitive dissonance from a distance and if you have to deal with them, then try to absorb some of their negativity. The article suggests pretty much the same.
1. Keep emotions out of it.
2. Don't attack. Discuss.
3. Listen carefully and try to fully understand the person's perspective.
4. Show respect.
5. Show that you understand why the person might have that opinion.
6. Try to show the person the facts and that the facts do not really change that person's view of the world.
Scientific American: How to Convince Someone When Facts Fail