OK so I met this girl 2 years ago, we slept together, but we lived in different cities.
Now I moved back to the same city and I want to be with her. We slept together again but I found out from a friend that she thinks I'm in love with her and she's not ready to be in a relationship.

Now it's a little complicated because I told her last night that I have insecurity problems and instability problems from my father being abusive when I was growing up.

I told my friend who said I should never tell a girl my problems, that they will always think in the back of their heads that I'm unstable. I know she still likes me, but can I recover from what I told her? Will she ever consider me boyfriend material? What should I do?

Yes I think you can recover for now respect her wishes and not rush into anything with her. If you try being her friend and not bringing up you wanting more and hanging out and not pursing more than she wants in time she will see if you are or not the man that she wants, at the end you will get to know more of her and she will get more of you and you never know... you may be a really sweet person and her expectations of the man she wants. That's mah thoughts on it, I could be wrong but don't worry you will find someone that's better for you if it doesn't work out for you all. Good luck! :)

Maybe the two of you should stop this friends with benefits thing because it only confusing things.

Be friends, just friends, and to be honest I would question her on what she said to your friend. Even if it is done in joking matter. Something like "Hey, I heard you thought I was in love with you?".

Btw, friends confind in one another so if she is using your past against you (which you had no control over) then you shouldn't even consider wanting her as a girlfriend.

This girl already told you want she don't want so maybe you should find someone who wants what you wants. There is a heavy supply of girls around.

Just because you are friends with benefits, it doesn't mean she will want a relationship eventually.

You should definitely stop this arrangement. If you want to recover, then do more talking with her. She said she doesn't want anything serious, so take it slow with her.

If she doesn't want to slow it down and just wants sex, then you don't need to bother anymore, you can just move on.