David knows he's doing the right thing by leaving. No matter how much he doesn't want to, it's the right thing to do. Staying would only break them completely in the end.
When it comes down to it, they were friends from the start. If they can't be together as more than that anymore, at the very least he wants to be able to stay friends with Neal.
It's not the first time they've fought like this, and it won't be the last. But maybe if David leaves now, goes to do the promo work that the rest of the band isn't really needed for, and gives them both some space, things will work themselves out. He hopes.
Neal hasn't spoken to him since he had told him that he thought Neal should stay at home, even though the plan had originally been for them to get away together, to work things out.
When David closes the door behind him, he knows Neal is up in their bedroom window, looking down at him. He has to fight the urge to turn around and look up at Neal.
This is what's best for both of them, and he knows that Neal will be there waiting for him when he gets back. Hopefully, that will be enough. Hopefully, the distance will have worked things out for them.