I think there is a bit of muddy waters here!
There is a difference in telling a farrier to do a trim, or a shoing job, that goes against what is best for the horse, in order for some show/performance goals, and perhaps having input, that is based on many years of trimming horses, studying latest hoof research info.
Afterrall, there is a reason that the barefoot movement got so strong, and often spear headed by former traditional farriers. Many horses were being lamed by bad farriery, and even Dr Stephan O'Grady, himself also being a farrier first for many years, before he became a vet, and who now only has to consult the vet and the farrier, in himself, far as any shoing approach in his equine podiatry practice, as he shoes the horses himself, based on his veterinary knowledge,lists the number one cause of lameness in horses is "BAD FARRIery.
Many people also think because a horse is kept sound in shoes, he is truly sound, and this is not so. Shoing can often cover a major hoof pathology, until the point is reached, where those shoes can no longer compensate
When I had breast cancer, I did not tell my doctors how to treat it, but I did do research as to options, different treatment protocols by various specialists,based on tumor grade and other factors, and then chose what worked best for me, far as re -occurrence risk , versus side effects
Working as a lab tech, I can re call a mother, not wanting to insult her family doctor by getting a second opinion, thus questioning that doctor's diagnosis.. He told her that her son just had growing pains. Not until he was walking the floor in agony, during the night, did she seek a second opinion. The child had osteogenic sarcoma,in one arm, which by then had spread to his lungs
It is not so clear as just firing a farrier, if you think perhaps he is not doing a good job, as he might be doing a very good job, as per how he was taught, but does not mean you can't ask questions, have input, esp if that is based on some true knowledge
My farrier certainly does not mind that, always compliments me on how good I have my horse's feet looking, and asks my opinion.
For instance, Charlie has one club foot, thus two front feet at different angles. Many people want their farrier to make those feet look the same as possible, thus he asks me, 'what do we want to do here"?
I tell him that I want the feet to be trimmed and shod for functional soundness, allowed to be different as needed He agrees that it is a good approach, and happy to shoe for someone that realizes this factor, versus expecting their farrier to make those feet the same, by either leaving the heels longer on the non club foot, or taking the heels down on the club foot below live sole, and to where the resulting pull by the DDFT will be exacerbated.
Curious as to why people think it is fine to perhaps question their trainer, but a farrier is beyond any mortal input, where you just turn your horse's feet over , Carte Blanche
Sorry, I did that in the past, and learned through the school of hard knocks, that some actual hoof knowledge, so you can at least recognize, understand what that farrier is doing, far as knowing the landmarks that help identify internal structures, and then perhaps at least ask, if that farrier is trimming contrary to facts you have learned, is not a bad thing. He just might have a very good reason, presented correctly to you, and thus help you in that hoof knowledge journey