On the radio this morning I heard some researcher from Washington University talking about how he studies factors leading to human aggression so he can figure out how to eliminate it. I'm not sure that would be possible, but even more importantly I'm don't think that eliminating aggression from the human species would be desirable.
What is aggression anyway? Physical violence -- and the threat thereof -- is major component, but there are also other forms of aggression such as social and economic. The key component of all forms of aggression is an attempt by one person to gain an advantageous position against the will and interest of another person. In order to gain this position, the aggressor signals that the aggressee's cost of resisting his action will be greater than the cost of submitting.
People tend to dislike aggression for two major reasons. First, no one likes having to choose between two bad situations: either you submit to another's will against your own interest, or you fight. Second, the aggressor's signal that he is willing to fight is much cheaper to him than an actual fight would be, but submitting is generally only a little cheaper to the aggressee than would be fighting; therefore the aggressee (rightly) perceives that the aggressor reaps the majority of the profit in the transaction by attaining a valuable position at the aggressee's expense for little cost.
Societal toleration for aggression varies from form to form. Americans tend not to put up with people who are physically aggressive, but we highly prize aggressiveness in our competitive capitalistic economy. Aggressiveness rules the roost in high school society, but adults tend to be less socially competitive and less tolerant of social aggression. Many sports and games foster tightly constrained aggression (physical and otherwise) that only rarely spills out into the real world.
It's certainly true that some people are aggressive in inappropriate or unwarranted circumstances, but as the examples above illustrate our social and economic systems tend to do a good job of punishing harmful aggression (though no one knows why it works.) Condemning all aggression and trying to root it out of human nature is a fruitless and counterproductive task, and reflects badly on the scientific process as a whole. The role of science is not to prescribe, but to describe, despite the fact that many modern scientists cast themselves as social activists or politicians.
That said, how aggressive "should" people be? Take the question two ways: what level of aggression is best for the individual, and what level of aggressiveness is best for society?