Well obviously I wouldn't think so!

No, I don't think it's weird. I think it's a positive thing to have therapists who've "been there" and can really understand. Only if they've worked on their own issues, though, ya know? I'm working on mine so that I can be as psychologically healthy as I can before I become a therapist.
Thanks for the advice about scars. My advice to you- if you want to go into psychology, (obviously try to quit cutting, but if you can't...) do NOT cut where it's visible. Try to cut where you can hide it. I hate that we have to do that- we shouldn't have to. But it's a fact that some people will judge you because of your scars
Good luck to you!
Angela