Issue with Break-up?

So in mid April, I broke up with my girlfriend of 4 months. It was really tough and now I don't think we're even friends, we've made both of us cry a lot. The thing is, I've given her my apology and reasons why it didn't work out and how I want to fix it. I even wrote a well thought out apology letter addressed to her mom and her. She blew off those apologies like they meant nothing to her. I sent her a friend request on Facebook to be nice, she claims she might hurt her other friends feelings if they know we're friends again. I get that she's had enough of me and wants a break (permanently maybe?), but is having revenge on me necessary? Will it stop?
Eventually, I want to start hanging out with her and hopefully trying again but she seems uncomfortable with that (rushing). I don't know why I blasted my anger on her ending the relationship, I think it was I wanted revenge because I didn't feel loved but it was a wrong decision. I still like her a lot and I wish she could see I didn't mean what I said and how much she means to me.
Issue with Break-up?
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