Welcome to high school, this is what 90% of teenage girls do. To be honest they don't actually have much feeling for the boys that break up with her/she breaks up with, it's more of a "Why can't I get a boyfriend" feeling, and along with that, they are simply doing this to bend YOUR emotion around them. If they can come up to you every month, whine and cry and sob about their boyfriend, and then you say "Oh I'm so sorry, I feel so bad for you, I hope you feel better, cheer up!" then they have you by the loving balls.
My way of avoiding this is by
... Not caring.
BUT, if it's a legitimate story, they've been dating for 6 months and they had a truly romantic relationship then actually feel sorry for the girl. Comfort her and everything. But if she's dumping a guy every 4 weeks, don't care, or else she'll bend your emotions to her favor.
Every girl in a nutshell...
This is very false. There are girls who are like what OP has described but there also are many who are actually sensible, proper, well-caring...
forget, who am I kidding, 99% of the girls in high school are exactly what the OP described. I suppose I'm quite lucky that the girl I got is a one-in-a-million type who's basically the best of everything.