While I agree with you, and would love to see Wolverine removed from the Avengers...
... Steve Rogers and Tony Stark invited Wolverine on to the Avengers in the first place so Wolverine could make the tough decisions that Steve and Tony couldn't. In other words, to do the dirty work while they wash their hands clean. (It's much the same reason Cyclops gave to Wolverine when he asked him to assemble X-Force in the first place). Given that that's the case, it would be hypocritical of Steve to judge him or accept his resignation on this basis. They knew who he was when they invited him on the team - in fact that's the whole reason he was invited in the first place.
I'm not saying it was good writing, but there it is.
This wasn't "dirty work."
This was revenge. It was specifically not the sort of thing Tony, Steve, or Scott "hired" Logan to do.