What does being "cold" have to do with being "detached"? Has someone here advised you to be cold?
Honestly, it sounds like through your actions, she can live the best of both workds. She gets OM and you're still hanging on her every word. You can't BEAT OM. The way I see it, the only way she will consider you right now is if OM ends it with her and she comes back to you. Is that ok for you?
