There are several elements of your concern that I think deserve some review. First, this is a long-distance relationship with a man that has cheated on you and has told you he can’t love you the way you need to be loved. In addition, he cannot be vulnerable enough to tell you what causes him to be this way. You are saying you want him to prove his loyalty, but everything about his fidelity, location, and emotional availability suggest you are more drawn to his potential than his truth. I don’t think you are pushing away a good man as much as not seeing who he is.
I’d recommend individual therapy to understand more about this. The Find Help tab at the top of this page can help you find someone in your area.