My friendship is over after 10 years and she refuses to talk to me. Am I wrong?

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Last month a friend and I got into a argument and now she tells me the friendship is over. We have been friends for over 10 years. The argument started because I was hoping to spend time with her at least once this summer and she was telling me it wasn't possible. She started making up excuses like she always does and even lied to telling me she just got married. I know very well she isn't, but this is the extreme she will go to for things to go her way. Last year I tried to spend time with her and we even made plans, then she canceled for no reason. It seems she only wants to be my friend when convenient for her and if I try to make plans with her she will not be bothered. If she wants to do something on the rare occasion, I have to drop everything. She ditches me for other people and is never there for me like I am for her. Also lies to me. This has been going on for years and I had enough. So I told her that I was tired of her treating me like dirt. Words were exchanged and I told her I hated her and that pissed her off. I really didn't mean it, but I was just frustrated of being treated like a doormat. I called her the other night so we could talk. She said she would call me later and she never did. So I texted her asking why didn't she call me back. She said that we have nothing to talk about and the friendship is over. She wouldn't even call me and tell me this. She used a lame text message like a scared cat. I understand I shouldn't have said mean things to her, but I was angry. She has done worse to me and I forgave her. But she refuses to do the same for me. I finally stood up to her and I guess she doesn't like it. If she was really my friend, why would she end a friendship of 10 plus years. I was always a good friend to her, but she was never one to me. I guess I didn't mean anything to her. It still hurts. I sent her a letter and she should be getting it soon, but I don't think it will do any good. Seems to me she took the easy way out. Sometimes I wish I never said anything to her about how she was treating me. At least we would still be friends now. I apologized to her, but she doesn't care. She is the kind of person that if you cross her once she never forgets it. Very unforgiving. Did I do the right thing?