There is no such thing as being friends with an ex...
I'm sorry but there isnt, and it doesnt matter how long it was since they broke up or blah blah blah either. If shes not willing to drop this guy for you, then there is a problem and you need to leave. Dont give her the choice, shes already made her decision. You need to tell her what youre going to do and do it.

I've tried the same thing...being friends with an ex... always end up back with him. Always. And I am extremely strong willed and strong minded.
Youve already lost her if shes to the point where shes arguing with you over this guy. He shouldnt even be in your every day conversation. He shouldnt even be around.