Short version: I am left-handed, but right-armed, and chose to be functionally ambidextrous, with my important weapons, at age 22, in 1983.
Long Version:
Texas did not have general legal concealed carry, for private citizens, when I came of age, and, I grew up in a gun-free household, so I did not establish a strong or weak side, until I became a police cadet, at age 22. I was left-handed, and left-eye dominant, but was right-armed, when throwing, or using larger tools. I had bought a 1911, at age 21, and already being interested in entering police service, so, I shot this 1911 both left- and right-handed.
As a teen I had helped my father build his rather large house, a multi-year project. It was expedient to be able to wield a hammer with either hand.
Well, upon entering the academy, an S&W L-Frame is not exactly a small tool, and long-stroke DA is not exactly a fine motor skill. Drawing that L-Frame, from the then-mandated low-slung, swiveling duty holster was not unlike throwing. Being employed by a PD, in which patrolling alone, in a vehicle, was the norm, the right hip is more accessible, as one arrives on an incident. So, I chose to carry “primary” at 0300, and chose to train to shoot well, with each hand.
Today, I am functionally ambidextrous with all handguns. I dislike every ambi-safety set-up I have handled, for 1911 pistols, so tend to be “righty” with the 1911, though some of my best slowly-fired 1911 groups have been fired lefty. DA revolvers, my first mandated duty handguns, remain either-hand guns, except for the little ones, which hurt my aging right thumb/hand/wrist. I shoot Glocks, and single-action revolvers, better lefty.
I am now retired from LEO-ing. 0300 remains my default “primary” carry position, but my right shoulder, gimpy since I was in ninth grade, has good days and bad days, and is getting worse with age. One reason I often carry two guns, other than the “back-up” factor, is so that my healthier left hand and arm can do the heavy work, and my larger handgun may be carried for expedient lefty access, if not actually on my left side, due to decreasing range of voluntary motion in my right shoulder.