To be honest, when someone says that they still want to be friends with me after I've initiated a breakup, I usually find it to be code for: I'm going to wait around pretending to be friends with you in hopes that you'll change your mind.
I've tried to be friends with exes and it's never been possible for me. I don't relish having to reject the same person over and over. Better just to move on and let them move on, too.
“Inside every cynical person, there is a disappointed idealist”--George Carlin