Why right cerebral hemisphere control left side of the body same thing for left one?

Answer:
It is a curiosity. In the spinal cord and lower brainstem (pons and medulla), both sensory and motor structures are on the same side as the part of the body they innervate. Then from the midbrain on up, sensory structures start to have this backwards, and in the cerebral cortex, it's almost all backwards. Somewhere in the evolution of these higher structures of the brain there was certainly a good reason for the switch.

It may have been when the colliculi evolved in the midbrain, the inferior one for hearing and superior one for seeing. The former receives input from both ears so we can locate where a sound is coming from. The latter is involved with locating something interesting visually and moving our eyes there. It's input comes mostly from the eye on the other side while it's output goes back to that side. So the left superior colliculus will see something interesting in the right side of the world and signal cells in the right side of the pons to drive both eyes to the right to see it better. There is then motor information that crosses back to the left to move the left eye to the right as well as motor information that stays on the right to move our right eye to the right.

In coordinating either of those functions for our two ears or two eyes, something had to cross the midline to make that work. For some reason the colliculi formed so the sensory information crosses the midline, then the motor information gets relayed to both sides, as it has to for us to turn well. I don't know that anyone knows exactly why that option developed as opposed to having only motor information cross.

Once the midbrain has crossed, it's easier if everything above that is crossed in the same way as the colliculi, which it is. So however it happened there was one event in evolution that crossed the nervous system at one level. Essentially everything above that is crossed. Essentially everything in the nervous system below that is on the same side as the body.

The corpus callosum just connects the two cerebral hemispheres. Connections between the cortex and lower structures have different names.

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The neural connections all cross over at the corpus callosum (the "division" in the center of your brain).

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Yes the wires do cross over to the other side. Since you are in the nut room look at where the nerve wires go under the two brain hemispheres. It all goes through the auto brain or the lower brain. When chemicals in the brain fluid are too high from erasing expectations the auto brain can access all those wires and you will be totally nuts too. Well now you know the rest of the story.

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