Does levelheadedness equal agreement to you or something else?

Often in the non-Fluther world, there are people I stop talking to, or don’t talk to much because they are not levelheaded. People seem to think it is because they do not agree with me. I tell them it has nothing to do with agreement, but with temperance. I don’t care if you disagree so long as you can do so without getting indignant or obstinate. If you can’t debate or argue your point without getting angry or sinking to insults, I do not see you as levelheaded. One can be illogical, and they often are, and still be levelheaded. Where do you set the bar for levelheadedness?