Slowly -- Gosh, I see so much potential here! Even talking about how to talk about it is a step forward, no? (yah, ok, I know what I meant! )
It seems like you both are being pretty clear that you are hurting right now. And h is pretty clear that he feels that he is hurting PLUS reeling from the added "bonus" of having hurt you as well...it's an interesting point, actually, one that I hadn't really considered.
Anyway, it seems to be coming down to two different styles of "dealing" with it, right? Yours appears to be focused on talking it out while his is internal. No doubt he's also suggesting that talking YOUR hurt out adds to his since he's identified that added layer on top, no?
Couple of suggestions come to mind...validating his desire to NOT talk about it and trying to glean what it is about talking that feels negative to him (one thing that leaps out at me is that he seems to feel that talking is "pointless" -- that there won't be closure from it anyway so why do it? maybe it would help to have a clearly defined "goal" or "solution" for the conversation? Even putting time limits or something like that? I could see doing something like "I'd just like to talk freely for 5 minutes with the goal understanding XYZ" where XYZ is some specific point). Asking him "what would feel ok for you in terms of a conversation?" or even really highlighting to him (and I think you did this well already) that it's the act of venting/talking that seems helpful to you NOT that you're looking for a solution from him. Even presenting it to him as "look, we're on polar opposite sides here about what we think we need to heal...what do you think would be an acceptable medium?"
I think if you can address his feeling that it'll just be an endless cycle you can get somewhere...also, highlighting that you're not looking for a solution...and recognizing that his way of healing is AOK, too, but that doesn't mean that you HAVE to do it that way too.
Sage
Relax. Appreciate. Be calm. Laugh. Enjoy. Be secure. Be loving. Be loved. Don't personalize. Don't ASSume. Accept. Be grateful.