Ok, she's a fighter. She likes fighting, she wants to fight. But I couldn't tell you the reason why.
Maybe she has intimacy issues, like she is uncomfortable getting close. She doesn't just give away trust. She is provoking to find boundaries. When people fail her tests, she can't trust them, so there is no friendship to continue building.
Or she is awkward and doesn't know how to interact normally. She learned this from her parents. Her parents failed to provide a stable relationship.
Or she needs high-intensity interaction. Normal interaction is boring, lackluster, and it just doesn't give her what she needs. That's like the adrenaline-junkie personality. Is she intense in other ways? Lots of physical activity, daring behavior? ADHD?
Or she is a narcissist. These people are really dangerous. They are always in it for themselves alone. They manipulate everything to their own advantage. Con artists. They re-write history for their own benefit. But they usually pretend to be sweet and trustworthy. Very charismatic. Will attract a following. They will take advantage of you. These are the people you need to stay away from.
So the question is, is this friendship doing YOU any good? Do you like it? Are you standing up for yourself? You need to say something if she is being mean. If she wants a sparring partner, and you want a sparring partner, this is good. Tongue-in-cheek insult wars can be really fun. If she is provoking you as a test, she WANTS you to stand up for yourself. If she is provoking you out of malice, you need to stand up for yourself. Don't be friends with someone who just wants a doormat. Shut her down.