My friend get's mad because of this?

I have a friend who is very very sensitive and will blow up at you if you tell her you can't hang out because you're going to see a movie or something with someone else. I was hanging out with someone I know and we called my friend to ask if she wanted skype. She got so upset that we were hanging out without her that she said "Never call me again. That was so mean of you to call me". I always end up having to apologize. Does anyone know what to say or do in order to get her to see my point of view without making her blow up at me? She would also get mad at me when I wouldn't be able to wait for her after class to head to my locker. She would hold it against me as well if I went to my class before she did. I don't know what to do anymore? Please PLEASE help!!! I've tried to talk to her but she won't change at all- any other ways??