Well, first things first.
As Fa_jing said, boxers aren’t lopsided (excepting pershaps Sonny Liston), but they throw punches differently from one hand to the other. It’s simply a question of goal-- do I want to use the jab to gauge distance, to stop an incoming attack, or to do heavy damage? If I can get away with it, I’ll throw a jab with lots of torque and drop step into it, which is a power punch. But since most boxers will read that a mile away, I’m forced to use my jab in a more speedy fashion to set up my right cross, right uppercut, and rear hook. This is what I mean by lopsided, tactically. I can hit hard with my left, but I hit hard more effectively by setting up a strong right hand with a speedy (but weaker) punch from my left to open the door. Since it’s more tactically sound (for boxers) to fight this way, this idea becomes ingrained pretty quickly. It’s not that I won’t be able to hit hard with my left without a setup should the need arise, but unless I’m sure I can get away with it, I tend not to do it.
This tactical view point is part of the problem with boxers who decide to “switch” stances from orthodox to southpaw in the fact that your defense and tactics completely change when you change it up. You have to dodge differently, change your combos, watch your footwork, etc. It’s not simply a matter of doing mirror images of your orthodox stancework. It’s about learning new tactics, new footwork, new combos, and new bearings in the ring.
Personally, I’ve been playing around with fighting southpaw because it makes my Shuai Chiao throws easier to get; however, if I was to try to enter on a pure orthodox boxer southpaw, I’m sure I’d get eaten alive. If I slip a jab, I’d have to worry about moving right into the path of my opponet’s cross, rear hook, overhand right, etc-- in other words, his power hand. I’d have a better lead hook and maybe a slightly heavier jab, but I sacrifice a lot of familiar training and tactics for two dubious advantages.
However, as a final point, lemme stress that there ARE boxers who can switch it up, or fight strong-side forward. Paul Spadafora (yay Pittsburgh!) comes to mind, especially. If taught this way early on, I think it makes for an easier time switching between the two. Unfortunately, most people cannot make it work for whatever reason and tend to fall back into the strong/speed divide.