Get / Give a move-out date or say you'll be moving and the house will be put up for sale.
But don't do any of the above unless you mean it.
You can take control for yourself since he is just walking out of the room.
It is pretty typical A behavior--please don't take it personally.
He doesn't want to deal, so if he walks away he buys himself time.
I suggest you don't let him get by with that if it is hurting you so much.