I generally carry two of the same weapon: SIG P229. I have to be careful not hurt the feelings of one, by calling one a back-up, and the other primary. I would not want one to develop a complex or anything like that. Seriously, the one on my right hip is the closet to being a primary, because I virtually always have one handgun there.
As for being rightie or lefty, I guess I have "dain bramage." My left hand is more skilled, but it feels more natural to perform most whole-body tasks with my right arm and leg. Old chronic injuries have reduced my right hand to being weaker than the left hand, when hand strength alone is considered.
Why a second gun? Well, the FBI-v.-Platt&Mattix incident in 1986 can be seen as a microcosm of everything that can happen to one's right hand and arm, and pistol, during a gunfight. Look it up, and see how many of those folks were shot in a hand or arm. Look how many agents' handguns were lost or damaged during the crash and subsequent shoot-out. As I recall, without looking it up, two agents' handguns went astray during the vehicular collisions, one agent's pistol was hit by one of Platt's bullets, and two agents were hit in the hand or forearm, effectively disabling that limb for the duration. One agent who lost his weapon in the crash had a back-up on his ankle, which he did use.
It doesn't take a felony stop to cause one to lose a handgun that is not securely holstered. Ever heard of road rage? While it has always existed, it has become a trend lately.
One doesn't have to face a rifle to be shot in the hands or arms. I personally know two sergeants, at my PD, who were shot, and out of commission, after being hit in the arms. (One was hit in one arm, which shattered both forearm bones. The other was hit in both upper arms, breaking those bones.) Other officers with my PD have been similarly injured. (There are several thousand of us, so we are a pretty good study sample.) Both arms being totally disabled is an anomaly, however. Usually, it is just one, and one can still fight.
In the private citizen arena, I have taken reports from folks whose first awareness of an attack was a sudden rush by a bad guy that grabbed or otherwise occupied the right arm.
There is, too, a much more mundane reason I carry two service-type pistols. I don't have to worry about one being stolen during a burglary of my home or vehicle, if they are both with me. I do have a gun safe, but opening it two or more times a day is a bother. If I can avoid opening the safe so often, and boost my level of preparedness, by one personal habit, well, why not?
The flip side of carrying multiple weapons is maintaining control and possession of them. Gotta pay attention.