One word that came to mind was truculent : tending to argue or be bad-tempered; slightly aggressive, but I don't think it is strong enough for the behavior you're describing. There's more of an aspect of stubbornness to truculent than getting angry.
"Difficult" people can also be contentious or the type of people who like to argue.
I might also call them confrontational or people who enjoy confronting or opposing other people, but I also don't know if that's strong enough.
Another word came up when I was discussing this with my husband - Defensive : excessively concerned with guarding against the real or imagined threat of criticism, injury to one's ego, or exposure of one's shortcomings. This doesn't always imply angry and aggressive, but it is very closely related to not being able to handle people disagreeing with you. You might call him "aggressively defensive" and it would have the added benefit of combining two normally opposite words :)
In poker, we call them "rammers and jammers" - they play extremely aggressively by raising the bet and re-raising to scare other players out of the hand instead of winning by skill. They also tend to lose a lot of money against folks that play well and know their tricks ;) I don't think that phrase is widely known, and it might mean different things to different people if you use it outside of the context of poker.
The reason I think it fits is because people who get extremely aggressive when other people disagree with them are trying to "win" the discussion by overpowering the other person instead of using their logic.