The hardest part in learning math is learning math is not about me. Math is not about you. Math doesn’t tell you that you are wonderful. Math is not reinforcing you how interesting you are.
Without such reinforcement, people seek it elsewhere. If they can’t go elsewhere, they invent it. So they don’t see the answer or the mathematical logic or the mathematical thinking.
This is showing up in Keith Devlin’s course at Coursera on Mathematical Thinking. He has put out some questions and people are not able to come up with the proper analysis of them in some cases. Even when the proper analysis is linked to in the discussion forums, it is ignored. Even ignored in the same thread. Even when the thread title is about it.
People simply can’t get themselves focused out of themselves. This is why they can’t learn the right explanation when they have the wrong idea.
This is at the core of many societal and private problems. Companies can fail from this. This is the stuff of financial panics. When denial of reality can’t be denied, there is a panic.