Fab is pretty ballsy herself as far as what she'll say and who she'll say it to is concerned. Does frienemies sound good to you? Sometimes they agree and get along, but when they don't they go for the jugular. Fab is in Kennel Club too, strictly as a domme, so they'll at least have that in common!
I don't remember the origins either tbh, but giving Fab and Rosalind a bitter dispute sounds like fun to me. They share a maison and form, so plenty of opportunities for them to go after one another. Fab would take exception to Rosalind purely for being a halfblood and a newcomer. I could see Fab starting off with low level things like giving Rosalind the wrong directions to ensure she winds up late to her first day of classes, or helping her find the staircase that leads down into the dungeons vs getting to the dining room, etc.