Everyone can learn something from everyone.
Even the stupidest people have something to teach you.
No trainer, and no person, is an omniscient horseman nor rider. In my opinion, the best trainer is going to be someone who can take bits and pieces from every style and be able to adapt to each horse and rider.
For example, my little reining filly HATES it when you get after her for doing something bad. You have to ASK her permission for everything and correct it gently. I have gotten myself chewed out for not punishing her harshly for some of the things she does, but when I do she gets way more upset and gets worse. When I correct her with a lot of gentle asking she is much more pleasant and does better. She responds to "Natural Horsemanship" better than any horse I have ever seen.
While my Anglo Arab gelding, he is a dipstick. I have to use the crop, over and under, spur, and really, REALLY get after him. Natural horsemanship does NOT work with him and I have gotten enough respect by thumping on him some, and he does a wonderful job catching on very quickly.
I have seen barrel horses who are leaking out of their turns respond differantly to differant techniques. Another example,
My gelding would always leak out on the backside. To correct this I just made him turn it until he came out clean. Never had a problem again since we started doing it. HOWEVER, on my new barrel prospect, I have to stop and spin her towards the barrel to emphasize shoulder control. The gelding I tried spinning on too and he never got better, but the filly will get the message almost instantly.
Eveyr horse is unique and so is every rider. If you have honest, proven reason behind your method then I say go for it. If it works for you and your horse, then do it. But if you are paying to take lessons, I would take the trainers advice. Otherwise you are just wasting your money for their training when you have something yourself that works better.
Of course, just stopping and explaining your way might work too. A good trainer will explain everything to you. After you are informed on both methods for training the same thing, pick one. But just one piece of bad information does not mean the whole technique is bad. Jut like a basket of fruit - Just because one apple is rotten, doesn't mean they all are! Everyone has something to contribute.
Pssh.I didn't pick up the wrong lead
It's called a counter canter...
...A very advanced maneuver.