You're exactly right. He's not filing because A) he's a coward and B) he's pushing you to do it so he can say you are the one who ended things. BTDT.
I decided to call BF on his cowardice and end things myself because I had enough of his bs. As long as things work out better or just as well for you to keep things as they are then do that. {If you want to try to push him to file, try calling him a coward to his face. It'll at least give you a great expression to look at. Heh heh.}
If you love somebody, set them free. http://tinyurl.com/2empx2g