Understanding and updating beliefs on deeply engrained topics can take enormous efforts, but sometimes it can be so hard that the listener cannot even in principle accept the new reality. The listener is simply not ready, he lacks a vast background of reasoning leading to the new understanding.
What fact that you know is true but most people aren't ready to accept it?
By "you know is true" I really mean "you are very confident to be true".
Feel free to use a dummy account.
To be fair, my position is less described by that Quirrell quote and more by Harry's quote when he's talking to Hermione about moral peer pressure:
"The way people are built, Hermione, the way people are built to feel inside, is that they hurt when they see their friends hurting. Someone inside their circle of concern, a member of their own tribe. That feeling has an off-switch, an off-switch labelled 'enemy' or 'foreigner' or sometimes just 'stranger'. That's how people are, if they don't learn otherwise."
Unlike Quirrell I give people the credit for actually caring, rather than pretending to care, about people. I just don't think that extends to very many people, for most people.