WTF indeed. So he effectively broke up with you, but you argued with him that you all should make a more definitive split, to which he THEN refused to accept, instead only agreeing to some time apart to bone other people while trying to figure out if you all really love each other or are compatible.
What a ridiculous situation. It’s like the time when George’s girlfriend refused to break up with him on Seinfeld. Thing is, I also don’t understand what your problem is. So dude won’t specifically agree to the breakup the way you want to view it. So what? He’s basically breaking up with you anyway. Just take it and run with it. Why even argue with him about it. Methinks you don’t really want to break up and you wanted to give him another chance to say that he still wants to be with you. That’s the impression that I get.
What you need to do is take a break from him since that’s what he’s doing to you and then go figure out what you want to do with your life since you can’t let go of a man who wants to bone other chicks.