"that's who I am, deal with it" pretty effectively slams the door in your face doesn't it? It is easy (feels safe) to say that and walk away, but I have to wonder if she really likes being that way.
I will admit that I have behaved poorly (perhaps similarly) during some difficult times but I recognized it and was embarrassed by it and worked on changing it. My husband would say things like "you need to calm down" or "you're overreacting" and it would make me so much more angry but deep down I knew that he was right and I appreciated that he was still there trying to work with me in spite of my bad behavior.
For me, seeing that he kept trying to work with me, in spite of bad behavior, anger, frustration, fighting, etc. and hearing him consistently say that he loved me and wanted us both to be happy and stay in our relationship - that helped me to not feel so defensive and look for ways to be a different (mentally healthier) person in the relationship.