“No” is a delicate subject because it’s so bound up in trust and secondarily in ego. Too wrong a move on either the instructor’s or the student’s part and an otherwise promising relationship can take a hit it may never recover from.
The issue can arise in three different contexts: 1) business/logistical ones, 2) the instructor on the student’s horse, and 3) the instructor asking the student to do something she’s uncomfortable with.
Taking them one at a time, business matters ought to be the province of the student. You’re the “customer”, after all. It’s your money. If you don’t want to go to a particular show, if you don’t want to pay for an extra training ride each week, assuming you’ll recognize and accept the outcomes, that should be up to you. If the question is medical or related to a purchase, that’s why God invented second opinions.
When the topic is “Can the instructor or clinician get on your horse?”, I think implicit in your decision to get help from him in the first place is that you grant that permission. I always ask a rider first, but that’s only pro forma. Needless to say, if the answer is “no”, the atmosphere in the rest of the lesson will be very different, and there won’t be many more! One very prominent rider with two FEI horses confided to me that she would only take one of them to a particular international coach. He helped her a great deal with horse A, but when he got on horse B, he always made it crazy, and she didn’t want to be in the position to have to tell him “no”.
The third area of contention is the most complicated—honoring the instructor’s request when you’re mounted. Beyond any philosophical conflicts, this can involve a whole raft of health, welfare, and safety issues for the rider as well as for the horse. A couple of generations ago things were different. In a cavalry-rooted riding society, you simply did what you were told—PERIOD! Injured? Go heal and come back when you’re better. Modern riding—primarily recreation for mature adults—coupled with our litigious culture has changed all that.
Instructors can hardly afford to be wrong. Even so, we all hear some amazing horror stories: “He asked you to do WHAT?!!” Nevertheless, part of the teacher’s job is to push you beyond your comfort zone. The demand may be anything from “Send him more forward,” to “Use the whip,” to “Drop your stirrups.” Or even something as seemingly simple as “Ask him to canter.” A good instructor reads the horse, reads the pupil, and weighs the outcomes. Over all the years I myself admit to having been wrong in this regard a few times—fortunately not too many. Unless the instructor is a total jerk, a wrong judgment with a bad outcome should weigh as heavily on him as it impacts the student herself.
So, yes, it is OK to say “No”. You better have a really good reason. You better expect to have a discussion about it. And if your instructor’s rationale makes sense, you better be willing to change your mind. If it’s a confidence issue, “no” may be provisional, not categorical. The instructor may need to lay more groundwork or approach the problem a different way until compliance sees less threatening to you. If your instructor can’t cope with a relationship more nuanced than blind obedience, you probably need a different mentor.