In the old days you turned a fighter around, a lot of it being because it was hard for a leftie to get fights. that is why hagler learned to fight both ways. Now, there is a thing among boxing trainers to let a guy go with what is natural, so you see more lefties. But a lot of that is laziness/ignorance on the part of trainers and i think it hurts the quality of boxing overall because, in general, you don't become as skilled a fighter as a southpaw as you could have otherwise.
that comes down to a misconception about what is important for a fighter. A lot of guys turn southpaw because they hit harder/more comfortably with their left hand, so they box that way and their front hand never gets developed. but here is the thing...In boxing, 80% of the work is done with the front hand, the jab, the hook and so on. The back hand catches, blocks, parries, and sometimes punches. So there are a lot of guys, even upper level pros, that don't use their hands well, they look to potshot the left but don't jab well, don't hook well. They end up being very limited as fighters.