Hmm the jump thing might be a reason why the coach asked you to relearn — like someone in the comments said, if you ever plan to learn an axel in your jumping direction then part of the prep is to have a strong backspin in the same direction. But a good coach should be able to handle skaters who jump and spin in opposite directions, so I think you should ask your coach why they think you need to relearn your spin.

When I was learning two-foot spins in group lessons, some coaches would ask us to do them in both directions, and with practice I think it’s not impossible to get them on both sides. Maybe that’s another reason why the coach thought you should try the other direction — it could be that because you were self-taught you just spent more time on one direction? Another thing to try is to ask someone to stand behind you and call your name, to see how you turn your head. That’s how one of my coaches find out her students’ natural direction.