GHoST:

She has, either A) been in a family where one or other of the parents has cheated on the other - or both, or B) been cheated on herself.

You should either A) talk to her about any issues she has, and express to her that her possessiveness is causing you to be turned off, or B) don't get involved with her.

Maybe that is too simplistic, but I hope it gives you some direction.