Of course she's angry. She's a spoiled child and isn't getting what she wants, so she throws a tantrum. I'm guessing you're like a lot of us LBHs here and you're some degree of Nice Guy, and have probably spent years trying to minimize conflict in your relationship. So naturally, she thinks that if she creates conflict, or threatens to, you'll cave and she'll get what she wants.
I agree with LH that you need to work on this. You WERE baited and you took the bait. I know how hard it is to NOT take that bait, especially when it's nice juicy bait that has "hypocrite" written all over it and it's SO DAMN HARD not to point out what BS that bait is. But remember it's a power game designed to draw a reaction, and you reacted, so you "lose."
Hang in there, man. You can do this, and I promise it gets better.