Suppose I have a long-held and dear belief that thousands of years ago humanity was deposited on this earth by aliens.
Suppose I raised my children with this belief, and that my only friends are those who hold this belief and no other.
Now suppose a scientist discovers evidence that humanity did not emerge from an alien laboratory but was in fact created by a supernatural being.
That discovery is going to make me unhappy. I built a life around my beliefs, and contrary evidence is going to undermine that life, and my happiness along with it.
Being an assertive sort of chap, I go on the offensive. I'm not a (creation) scientist so I can't dispute the evidence on its merits. Instead, I go for the scientists credibility and speak out with hostility about the scientists personal life. I spread gossip and rumour about the scientist. I organise angry rallies, and I raise funds to have the scientist's work put under negative scrutiny.
In this way I resolve the dissonance and my happy life resumes.
Depending on my circumstances and personality I might have chosen other ways to resolve the dissonance. I might even have adapted my belief somewhat, changing my position just enough to accommodate the evidence.
Or I might simply have called it bullshit and walked away.