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I told you before: get out of it and don't waste your time any longer mate. Come on.
+1 to everything Poet said as well.
The ONLY correct response to the girl saying "we're done" is "ok see you later" while showing her the door. ANYTHING ELSE, from "talking sense into her" (i.e. pleading with her to reconsider) to getting angry to calling her a bitch, doesn't do ANY GOOD. None.
The more often she does it, and gets away with it, the MORE she'll do it, and keep doing it. She keeps picking fights because you ALLOW her to keep picking fights. She is testing your dominance and you are showing yourself to be WEAK.
You HAVE to show that, at any point, for even the smallest reason, you are perfectly happy to walk away forever. Her fear of losing YOU needs to be much stronger than your fear of losing her, and thus her motivation will be to please and respect you, rather than KNOW that she can disrespect you as much as she likes and KNOW that you'll put up with it regardless.
I learnt this lesson about 6 months ago with a girl who was completely my type and really really hot, but quite emotionally troubled. She had come out of an abusive and turbulent LTR and was really scared about getting hurt again. Quite early on, she tried to break up with me because I gave off too much of the player vibe and she needed commitment. Stupidly, I tried to convince her to stay with me for this and that reason and asked her to calm down and be reasonable. But that would only work for a little bit before she would do it all over again.
It wasn't until I said "I've have enough of this" firmly and stopped trying to convince her to be with me, that she became shocked and immediately started pleading with me to take her back and that she'd behave. I was then free to set the rules and terms of the relationship going forward, and accomplished a complete power reversal from pleading with her to stay, to dictating how she would act on my terms.
It lasted another few months until she said she initially thought she could handle the non-exclusive thing, but it was starting to be too difficult for her. I said goodbye again. She lasted about a week before calling me and saying she still really really fancied me and couldn't stop thinking about me and would I please reconsider and she promised she'd accept the open relationship thing.
In these instances, my power to dictate the terms came from my willingness to put an end to her behaviour and walk away if necessary.
Whether you want to stay with her or not, the BEST thing you can do is tell HER "it's over" next time around.