Well, I haven't seen this theory anywhere else... so here is what I believe..

Basically it’s from the time we were amoeba and then fish type things swimming in the ocean.

If you want to escape something then it’s the side furthest away from the predator that needs to kick into action. On a fish that would be the right eye kicking in the left side fins or vice versa (Those fins are supposedly our arms and legs now). However if we regress back a bit, it would be the amoeba touching an object and the other side of the body contracting and wriggling to move away from the object.

Nb: Have to be a bit careful though as it could easily be said that the side closest should contract to push away from an object as like a jellyfish. Which would making an interesting analysis is whether these type of biological mechanical setups have different coordination styles. Quite possibly the development of fins that progressed into limbs locked in an evolutionary pathway as no environmental consideration necessitated it once on land.....

As an analogy, consider you are in a rowing boat. If you see something on your right that you want to arc away from, which arm is going to kick and do the most action? It would be your left side.

The right controls the left and vice versa, it’s an environmental advantage from the most primitive times.