I completely agree @tarazkp, and it's a matter of communication where people actually listen to someone else's point as opposed to only figuring out their next retaliatory argument.
There's a little something I like to call fair fighting; no personal attacks, no insults, look for a compromise, like you stated here, agree to disagree when you can't meet that compromise, no generalizations, no degrading language, and if you're angry, wait to comment the next day when you've had time to cool down :) Works the same with relationships in our real lives as well I think.
They say all is fair in love and war. Love I understand because love is unlimited. In war however, it is only because of the fear of losing. When it comes to understanding there is no loser, which means in a good argument, I can lose and still win because my understanding has grown.
Bingo! but you are preaching to the choir here :) Why can't everyone just get this though? What a nicer world this would be...if only.