I'm going to break up with my gf because I've hurt her too much and don't think I can measure up to the potential she sees in me
What makes you think you're unworthy of her expectations?
I cheated on her with this girl
While it is difficult to admit, sometimes others expect more of us then we can be. It is okay if you think that your infidelity means that you don't meet your girlfriends standard and that she can do better.  But you should be honest with her about all of this.
So what you're saying is that I'm not good enough for her and she can do better. Then why is she with me?
I'm saying that we're all human and sometimes fail to live up to our ideals. That can be a tough lesson to learn in this case, but at least you should be open and honest with your girlfriend.