Starting over is usually when one person is cheating and wants to sweep it under the rug. That way if it is brought up in conversation, it can be said, "but that was BEFORE we started over"
She doesn't want to be in a relationship with you? because she wants other guys, but wants to be able to mess around with you.
so hey, if you don't mind being a booty call, and can use her for sex....then go for it...she made the rules.
Otherwise, I wouldn't waste my time with her if I were you. Getting mad at you for simply asking if you are breaking up? I think she needs to be put on the curb and she needs to know that she can't screw with your feelings like this....unless you just want to mess around and don't care that is.