It sounds like you have some really poor trainers, because not only is there nothing wrong with what you are doing it is something you should be doing.
Fighting is all about movement and body positioning. Your trainer doesn’t understand the use of stances and the interplay of body positioning, so he is trying to lock you into a limited form of fighting.
Your fighting should have a flow to it that should not get broken up just because you have the wrong side out and have deliberately trained to be an invalid in that position.
Contrary to what Otoko says maximizing your abilities will not make you a mediocre fighter it will do the exact opposite. It will make you a better fighter and give you an edge over mediocre fighters who have limited skills.
I know you’re coming from a TMA point of view, and what you say does make sense- the school that I was attending had us learning to punch and kick from both sides equally.
However, what the OP is old school boxing thinking. I’ve heard it quite a lot; for example,Joe Frazier turns around any fighters he has to fight orthodox regardless of whether they start off southpaw.
For one, it’s going to be harder to get fights- no one wants to fight a southpaw.
Number two- the skill set is so specific for boxing that I could see them not wanting him fighting that way. There’s different combinations and different movement associated with fighting southpaw.
This guy might think he’s fine at it, but the trainers might see that his footwork really revolves around being a righty. You never know. They might be trying to teach him the basics of the ring, and he’s switching feet all of the time, not allowing him to get perfect at the base footwork.
Number 3- I wouldn’t want to be a southpaw if I wasn’t one. Your jab doesn’t work as well, you get clocked with counter rights, and you really have to work on the “slick” part of southpaw. You can’t ever keep your hand in a low guard, which I really like doing, and you can’t hook to the liver, which is my favorite shot in all of boxing.
Just my take.