hmmmm, the fact that he is willing to surrender that decision making to another body over him (the Accords/UN Panel) kind of goes against that. You're missing out on the fact that the arcs Tony & Steve have been on have actually taken them to places where they are now the opposite of where they were several movies ago. I need to go see it again but from memory:
Tony is actually willing to be the opposite of what you say - "We need to be put in check and whatever form that takes, I'm game"
Where as Steve is now the one who is willing to act on his own decisions over listening to an external authority - "The safest hands are still our own"
This is pretty much the premise of the film, no? None of Tony trying to convince Steve to sign was for personal gain or to "prove he was right" or "get his". And when he found proof for himself that Bucky might have been set up for the UN bombing like Cap said he immediately went to Sam for info so he could go to help Cap.
It's only being shown a video of his dad getting his face cracked (by a guy he knew), and his mother get choked - combined with the fact that his friend knew and never told him that made him snap. In the earlier films I would absolutely agree that his actions were a liability. And we can go around the semantics of that a lot but I doubt there is anyone here who could have kept it cool enough in his position that they would be able to judge him for switching in the bunker. To call him volatile for that is kind of harsh.