Sorry to jump in near the end of this discussion...
I have been reading and I have seen some very good positions created, opposed, and defended. I have also seen some magnificent points made. The only issue I have with this is that the original question was "Why do humans fight" or some variation thereof.
I agree with TheRedeemed (two posts above) and that view on violence. I am a Martial Artist and was always brought up to use my strength to defend those that cannot defend themselves. I was taught to be polite, kind-hearted, and respectful, but that does not preclude me (or inhibit me) from learning multiple ways to kill someone with a single hand.
Violence is a necessary part of human existence. Whether it was designed that way, randomly occurred that way, or became that way (as your religion or philosophy demands) the fact remains that violence is the way of life now. But it is not the source, it is the effect.
In my humble opinion, that source is that living creatures sustain, improve, and define themselves through conflict. Previously there was a post that spoke of "the need for dominance" (sorry, I am unable to quote as I do not really feel like digging for it, I apologize), and that cannot be more correct. In large creatures, like humans, it is necessary for a pecking order to be established. That hierarchy cannot be created through calm and quiet discussion (as much as I wish it could be), or even through heated intellectual debates that revealed who is more capable of leading. More and more often it comes down to who has the strongest arm or the largest army.
Sure violence has occurred in our past, but why was it deemed necessary? The drive for control, power, and dominance is all important to humanity.
Take it as you will.