Why right vs left? What follows is pure speculation. Just as plausible as anything else, until further info:
In the early days, a "desktop" system laid down flat, and a "tower" was the standup things we see today.
The "desktop" was far more prevalent. Of course, you could stand it up if you wanted.
And there were no glass/plastic sides.
In this config, the motherboard was on the bottom, and all the components on top of that for easier access.
If you wanted to stand it up on edge...most people being right handed, would lift up the right side of the case. Resulting in the motherboard on the right, and the components on the left.
It just stuck, and eventually grew into the ATX standard config.
Go ahead, prove me wrong.