<human>: Can you provide a brief rundown of the text in within 3 sentences?

My best friend (21f) and I (21f) rarely fight. We're different, we disagree on many things, but we are usually very live and let live about it all, and would defend each other's idiosyncrasies to the ends of the earth. In general, I'm quieter, and she's more outspoken. 

A few days ago, I disagreed with her (unfair, I thought) evaluation of a situation. I told her why, and we didn't talk again for a while (not unusual, we don't see each other in person day-to-day). When I next spoke to her, and mentioned that her evaluation had annoyed me, she was flippant and joked about my feelings, which I took badly and left the conversation. 

I felt bad after ignoring her for a day, and tried to talk, expecting her to be angry but welcoming the chance to just talk about it and get it over with. The next hour consisted of her telling me that she had the right to be upset with me for disagreeing with her while I didn't have any right to be annoyed. I kept trying to respond with my feelings and actually work something out, but she kept responding saying I was being annoying and she had better things to do, and that she had the right to say whatever she wants. This is a common pattern for her, to ignore things she doesn't like, and I'm kind of offended that she'd refuse to even talk it over with me. 

So now, we're both properly annoyed, and nothing has improved. I feel like my only options are to apologise, when I'm not actually sorry for anything (except maybe being harsh at the start), or to try to fight again, which I fear will lead to one of us being provoked to say something horrible. How do you work things out in a situation like this? I don't know where to begin, or how to open, or what to expect. I'm willing to compromise (not that I know how here) but I'm not going to roll over and say that I'm wrong and she's right just to appease her.
<bot>: I scolded, she was offended, she feels wronged, I feel tired, and I don't know how to start talking again.