I'm going to refuse to apologize for yelling at my gf even if that means she will break up with me as a result
Why would you refuse to apologize for that?
I have anger issues
If you have anger issues you should apologize if you are wrong. You can seek mental help for the anger issues.
So why do I have to apologize even if I'm right?
It doesn't sound like you're in the right though beause you yelled at her, which you should never do. You should just say sorry to her.