While it sounds like your instructor isn't using bute in the best way, I personally don't have an issue with giving small doses of bute, when needed, to help a horse be more comfortable.
Most side effects of bute, from what I understand, generally occur after prolonged large doses, like 1gm/day for a year, etc.
My old lady horse has Moon Blindness so, per vet instructions, during an attack she's given 2gm/day which is A LOT.
As maintenance during the summer, since her eyes are extremely light sensitive, she gets .25gm/day (a very small dose) because otherwise she basically feels like she has a splitting headache all the time.
I get severe headaches myself and I know that if I were not allowed to take painkillers during a headache/migraine, I'd probably go insane from pain. Therefore, I'm not going to do that to my girl.
I do 100% agree though that bute should not be used to make an obviously lame horse sound or "ok" for riding. I think of it kinda like aspirin - you take it to be comfortable while in pain, not so you can rock-climb with a broken arm, yknow?
And bute should definitely not be used without a thought to the risks, for my old lady the benefits outweigh the risks (which are small given how little of a dose she gets) but it shouldn't be used as a "fix-all".
Fabio - 13 year old Arabian/Lipizzaner gelding
Hazel - 14 year old Angora goat
Atticus - 4 year old LaMancha/Alpine cross goat
Rest peacefully, Lacey.