I Can’t, I Don’t: 안 vs 못

Two forms of negation, both placed immediately before a verb or adjective:

안 – you didn’t do it, but you had the ability to
못 – you couldn’t do it because you don’t have the skills or ability

우유를 마셔요.
I can’t drink milk. (I’m lactose intolerant)

우유를 마셔요.
I don’t drink milk. (I think it tastes awful)

수줍어니까 자주 한국말을 해요.
I don’t speak Korean often because I’m shy.

한국말을 배워 본 적 없으니까 한국말을 해요.
I can’t speak Korean because I’ve never learned it.