I'm not a 4th level dressage trainer, but I do make my living with my horsemanship lesson business, and have been trained extensively in effective teaching. Granted, the vast majority of my students are children, but I have always been trained to retain my composure no matter the circumstances. In my experience, the moment you begin yelling at a student, they panic and shut down, their brains stop working, they become afraid, and do nothing. Clear, concise instruction guides much, much better. Preparation for these short cues are necessary for them to work, they associate the 5 minute explanation with the 1 to 3 word direction, and its less confusing. If all else fails, stop and recompose, re-explain, and try again. We were taught to remain calm and composed even in emergency situations, say for example, a runaway horse, I'm speaking loudly 'One rein stop', because they have been taught and have practiced it, not yelling "stop him!" Also, saying the same th ing over again, only louder, is lousy instruction as well. With the hitting, yeah, sometimes a horse needs a pop from the student, but we're going to be prepared for that "if he does 'A' you do 'B'" and then when it does happen, because they are prepared, I usually don't have to say anything, I just need to let them sort it out and correct the horse. If they do need to be told, I will say "correct him for that, that's not ok" if I find I haven't fully prepared them to correct the horse, we stop, explain, try again. No, I don't want the horse to get away with the behavior, but if they fail its not the horse or students fault, it's mine for not preparing them. I took one dressage lesson from a 4th level rider, and I never got the impression that she could make it from her calm, teaching tone to outright yelling.
A lot of people are great with horses, and just suck with their people skills.