It depends on the sort of argument I would be entering. For example If I was to come across a fool who randomly starts insulting me but doesn't actually know me at all, I will not react and "defend" myself because their words carry no weight as they doesn't know me and are thus not worth my time and effort.
I will enter arguments about topics that I have an interest in, when people seem to have valid reasons for their point of view, and will listen to them if they go about voicing their opinions in a civil manner. I'm not afraid to offer my own. I'm also quite happy to agree to disagree or admit that they opened my mind to something I'd never thought of before. I can't stand people who always have to be right.
It takes something really extreme from someone to irritate me to the point that I can't stand it anymore and have to say something to them, leading to an argument. I prefer not to start fights as most often you say more than you intend to in the heat of the moment and regretting it later can be too late. But then, I can't keep my mouth shut when someone is being unfair and I really believe in standing up for what you feel is right, but doing it in a cool and collected way (which of course, doesn't always happen).