You've got the case of one-itis for the ex.
The reason she still wants to "be your friend" is so she can have you as an emotional tampon when all the other guys who are f*cking her aren't talking to her about life, roses, and candy canes....that's where you come in as the "FRIEND"
And, the reason you are still wanting to be with her, even if its only as a "FRIEND" is because you one day hope that by being there for her emotionally, talking to her, picking her up from school and work -- that in the end of all these good deeds, she'll realize how great you are and come running back to you with open arms.
REALITY CHECK BRO..
There is a reason why you guys broke up....stick with that reason and move on. Yes, second chances with the ex do happen. I've seen the second time workout better for many of my friends. BUT, the one's who made it work the second time gave it months, even years, of being apart to realize that.
If you just broke up with her, and you're still around as a friend...she'll never truely see what she's lost.
My advice to you is to cut her off completely. YOU HAVE TO DO THIS! Keep busy, make yourself the busiest you can. Go out with old friends, join a gym, train for a marathon, learn how to dance, learn how to speak another language, learn how to cook....make yourself sooo busy that you won't even have time to be her friend.
The beauty part to all of this is that through this process, you will be BETTER than HER in all aspects of your life. And yes, there maybe that 7-8 months that have passed and you'll have dinner with the ex. But look at yourself now. A better man, a less needy man.
Nothing kills attraction more than a person who is needy. Trust me bro. Cut this woman out from your life and get busy! Busy with the things that will make you better. Do it for yourself, not her. When you start caring about yourself again, you'll stop giving a f*ck about her.