"An argument is the use of aggressive opposition to weed out weak logic, keeping the strongest ideas possible. The philosophy behind using arguments for problem-solving is that attacking the weak parts of an idea will leave the best solutions."
I'm with you so far. Being able to distinguish good from bad is the basis of critical thought.
"The metaphor for argument in our culture is war. We think of people we argue with as opponents ..."
I know a lot of people who do this, but I certainly don't, and I consider it a sign of maturity when somebody is able to separate ideas from egos. Remember, we started off by talking about the good and bad parts of ideas; not good and bad people. It's not a fight, it's a collaboration to share perspectives and discover new insight.
"... we attack their position and defend our own, we can gain or lose ground, and ultimately we can win or lose arguments—just like battles"
Whether you're focusing on the idea, or the person who generated it, there's really no use in considering them an opponent, and even less use in framing things in terms of winning or losing. Ideas don't "compete" with each other, any more than 1 and 2 compete to see which is the bigger number. There's only truth. If you're winning or losing, you've already missed the point and you're focusing on the wrong thing.
I think "aggression" is unfortunately not the real problem here, the real problem is that people often aren't mature enough to admit they're wrong, or to consider another person's perspective, or to say "I don't know".
I don't want to focus on this aspect of the article, but I find it really discouraging to continually see these articles which try to spin things in terms of gender. Developing this "men vs women" perspective is exactly the kind of "adversarial mind" the author denounces in the introduction.