[quote=@Balance]
<Snipped quote by Legend>

Let's see if I can continue, then. "I won't change." Neither person will change their ideas, and therefore--wait, no. I can't go from "I won't change" to "fight" unless we assume that I and the other absolutely have to decide which one is right. It doesn't account for the possibility that I don't care about the other person believing in his idea. Well, actually, that wouldn't lead to fighting in any case, so I don't need to account for that possibility.

[i]So,[/i] ignoring that tangent, let's assume that we both believe that only one of us can possibly be right, and that the other person being wrong is wrong. In this case, I will have to prove that I am right, and he will have to prove that he is right, so that each of us can correct the other's wrongness. This leads to an argument.
[/quote]

The other answer, by the way, is what you're getting towards. It's that every human has an existentialist need to believe their surroundings as real. We interpret our surroundings and consider our interpretations as our surroundings, so we believe what we believe to be real instead of what we believe. Two realities don't mix easily, and there are a lot more than two people. Ergo, fighting.