Should I make the first move?

I had a best friend, whom I loved to death. Last summer we got into a fight because I couldn't hang out with her because I had exams and she didn't. And she got mad and sent me a text that really hurt. We ignored each other for a couple of days, and then I decided to text her back. She didn't respond to that. At the end of the summer, we were still basically ingoring each other (she 'casually' commented on a few of my posts on facebook, and that's about it), I mailed her. I told her why I was hurt/offended and told her that I loved hanging out with her and that I couldn't understand why she was so so so mad because I couldn't see her. She mailed me back, saying that she never got the feeling that I considered her as my best friend, that I was never there for her, and that I couldn't show my emotions. She concluded with 'I don't want to friends anymore, but I just want to keep contact'. I was extremely wounded by this and deleted her from all the websites I had her on, and I erased her number. Till this day I am still offended.
I recently had a talk with a friend that knows us both about this, and she said that we're both acting like idiots and that we should make it up. It's not that I don't want to do that, but I'm too stubborn to tell her that I actually kind of miss her. She told me she didn't want to be friends anymore so why should I make the first move?