With untold hundreds-of-millions of people who use computer-mice, I can't understand how I could be the only one to figure out which hand to operate it with.

I guess blame goes to the guy who wrote the first mouse-manual - he just picked the thing up and, since he was a right-handed person, assumed that the mouse was meant to be a right-handed device.  If he spent another few seconds pondering the issue, he probably would have realized that the mouse was designed to be used in the SECONDARY-hand, rather than the primary.  Another slip-up in documentation was when authors insisted on calling the mouse-buttons LEFT and RIGHT.   Even the earliest mouse-drivers allowed for an interchange between the two.  Correct usage should have been, "mouse #1" and "mouse #2".

Consider the keyboard-layout.  The design is geared to RH people, with activity weighted to the RH-side.  Wouldn't it then be logical for any supplementary-device to be used in the other hand?  Some might argue that they can't do stuff with their 'other' hand.  This is not a valid argument.  The computer-mouse is not something that has an equivalent in the natural-world.  There is no 'instinct' that predisposes us to a certain usage.  However, the first five minutes a toddler spends with a mouse, will set the pattern for life.

Let's look at dexterity.  I am not an ambidextrous person by any measure, but since day-one of mouse-usage, I have been totally comfortable with the mouse in my left-hand.  Today, I can swap hands without missing a beat.  This would not be the case if the mouse only added exercise to my RH-side.  Taking a more gloomy scenario - if I ever lost one of my upper-limbs, I would still have reasonable computer-capability without retraining.

Epilogue: There may be a hundred or so right-handed users who believe they made the correct choice in following my early advice. When the computer-mouse came into common-use, I did contemplate taking up the crusade for its correct usage.  This did not eventuate - there were too many crusades in progress on other fronts [grin].