Mark: Can you think of a reason why the evolutionary development process would leave us with these two brains?
John Batson, Furman University: I think the key is just as you suggest, evolution.
Ancient ancestors that were the first vertebrates displayed bilateral symmetry -- the right side is more or less the mirror image of the left. And that held and holds true for most internal organs, including brain.
So long before there was anything resembling a primate (much less a human), our ancestors were selected for a bilaterally symmetrical body plan. By the time the first primate-like creatures evolved, the bilateral brain was almost certainly symmetrical in function as well. But with recent evolution (the last few million years or so), some functions became lateralized (right brain better at some tasks, left brain better at others). So the present human brain is a relic of ancient selection that has adapted to more current selection pressures, including especially language and bipedalism.
Why do we have two brains? Certainly, if we designed an efficient brain today from scratch, we probably would not end up with the existing brain... it is not completely intelligently designed. We simply inherited what worked long ago, and what got modified along the way.
And by the way, the corpus callosum is not the only fiber system connecting left and right brains. There are several other smaller "commissures" (connecting pathways) joining various parts of left and right.