Why all this fighting?

Name calling - wow, that is certainly a mature & sensible to way handle an argument/disagreement. Why do you even want to patch up things up with her when she is obviously an immature person who has zero respect for anyone.

I don't care how angry or upset you might be --- you do not, any under circumstances call someone names (at least to their face! ). Anyways, it your call. Maybe patching things up with her will keep you in good terms with your mutual friends. You could, just be civil to her and leave at that.

She is going to become more spoiled and bratty the more you play into her shenanigans. She should not be rewarded for loosing her temper and swearing at you. No matter what the circumstances were. Treating her to lunch is only going to reinforce her poor behavior/tactics. The only language she seems to understand is rudeness and bad behavior. If anything, she will be smiling like a Ms. Princess Brat if you treat her to lunch. Waste of your royal time and money. That is my opinion at least.

You haven't dated her yet, and look at her attitude/temper. Could you imagine what she would be like in a relationship? - NIGHTMARE. Based on what you have said, she sounds like a moody, unstable person with a lot of issues. Unless you are able to work around her personality/attitude then perhaps consider stepping away from this girl. Where do you think she got the impression that you hate her? Did you say something/or do something that may show that? Didn't get passed along through friends? - If is the third, is she so impressionable to believe what other people say without having adequate proof to back it up with? Are you prepared/ready for the continuing gossip that may take place between friends? Gossip that may trigger her temper and cause her to do something incredibly irrational. You go to ask yourself all these questions before you decide on offering Ms. Temper a lunch date.

Sounds like a similar situation I've been in. This girl sounds like she may have a little bit of a temper though. Maybe she's moody because she's hearing different gossip that may not be true (ie: you are mad at her). Try talking to her. Maybe try going up to her and asking " What's up? How'd you like the last party we went to? Thought I saw you there..." Maybe something like that to break the ice. Depending on how that goes, maybe you'll be more comfortable asking her to lunch for a future date. If you still feel things are awkward, maybe suggest you, her, and a couple of mutual friends go out for happy hour or something fun & casual setting. Good luck.

Don't act like I don't hate you so much that will show you like her too much and girls don't like weaknesses. Invite her to a party or something show her some fun. Cool?