One of the most beneficial truths I've discovered from living in Japan has been just this. Our typical, reactionary tendency to push back against whatever pushes us is, in most cases, the worst way to succeed, win, establish dominance, or gain anything in a negotiation (and any conflict is a negotiation). On the contrary, when we blindly react, we actually allow ourselves to be controlled.
I want you to try something. Really try it (not you, necessarily, rrjc, the general "you" out there). It will not be easy, because, for most of us, every fiber of our being screams out at us to do the opposite. Trust me, if you try this you will see exactly what I mean. The next time you get in a spat with someone: Apologize.
That's right. Say, I'm sorry. Say it before you say anything else. Say it sincerely and feed back to them what it is you are sorry about so that you demonstrate you actually understand and care.
Let me be even more clear: Say you're sorry even if the issue in question is 100% NOT your fault. Don't worry about that. Just apologize.
In almost every case, the person who confronted you will be so taken aback by your response that it will knock him completely out of "attack" mode. In many cases, he will actually reverse his statement, refuse to accept your apology, and then apologize himself for his own behavior. In either case, he is now in a different frame of mind, and when the both of you do talk now, you enter the conversation from positions of mutual respect and benevolence, rather than enmity and anger.
If you've never done this, it is absolutely mind boggling how effective it is. I actually learned it while dating my wife. Having dated only Western women up to then, I was used to butting heads about all sorts of stuff any time a conflict arose. However, every time I would go and bring something up, ready to jump on her (say, for example, for her making a mess of the house and my having to clean it up), she would just meekly, sincerely apologize. Now, all of a sudden, I felt like the big jerk for even bringing up such a petty thing.
Understand: This is NOT a demonstration of submission. This is an astonishingly effective tool for entering negotiations of every kind on equal footing. Even if something is not your fault, if you are both screaming at each other, not listening to what the other one is saying anyway, then what's the point? Lose-lose. This simple, contrarian response effectively disarms your adversary and turns him into your ally, or, at least, a less angry adversary who is still willing to give some ground to reach a conclusion.