Gf breaks up with me, wants me back, and then proceeds to flirt with others.

After a year and 4 months into my first relationship(both 20) my gf broke up with. It was the usual "I can't give you what you are looking for, and i only see us being friends."

I was obviously heartbroken since this was my first actual gf. I spent my summer working and didn't have much time to think about everything that occurred. Towards the end of summer i receive a text from her saying how we haven't spoken in such a long time and seen each other. Although not together, I still miss her and still seek her affection.I spend a few months(September till now) together with her and i develop all the emotions I once had for her all over again.

Two weeks ago I find out, from her older sister, that she likes someone else.This hurts me a little on the inside, but we still continue to see each other and she is still her lovey dovey self showing no difference towards me.

Last week, during a night out with her friends, few of whom i significantly dislike(she knows of this fact), she discloses with them that she only hangs out with me because she is forced to. Not for the sake of being with me, but for the sake of doing me a favor. I want no such thing.I only asked her to hang out with me because she generally shows that she is having a good time. Never would i have thought that she sees me as a pity date. I also learn of her flirtatious behavior with her friends whom I hate.Not only is she flirty with them, but she also proceeds to touch them, not sexually, but in a flirty way.

So reddit i ask you this. Should i just call her and politely tell her i want nothing to do with her anymore and just move on? Or is there any better advice. Thank for any input on this matter.

TL;DR:A girl who I have always treated nicely, breaks up with me because she only sees me as a friend. Later wants to go back out with me.While we go out the second time around, she flirts and touches guys I hate.