What in evolution caused the cerebral hemispheres to connect with the opposite side of the body?

Its a very interesting question and one that I have seen asked in the past. Don't recall the details but it may have had something to do with those evolutionary factors (pressures) that started the movement of eyes from the "sides" of the head toward the "front" of the face, allowing for true 3D vision with depth. The brain may have needed to cross information into opposite hemispheres in order to account for depth in vision, among other things.