Ask HN: Mathematicians are rarely the best math teachers but why

Because they're trained in mathematics, not pedagogy.

This is also not a math problem. It's a general STEM problem (I'm not even sure it's a problem, it's just a thing). The curricula is focused on solving problems and communicating the solution, but it is not focused on communicating the process of solving the problem. So why would they be good educators when they're not trained to communicate the process, but the solution, and education requires the former (among other thing)?

Mathematicians/most academics rarely have to explain things to people who don't know, or even worse, don't care

Teaching is a separate skill / talent. And it's rarely selected for in higher academia.

There's a significant difference among understanding, explaining, and teaching.