1. They are shy and/or introverted. They don't like working in front of an audience because they aren't good at communicating what's going on under the surface of the horse's experience or their own experience. They work better without distraction. They feel that people are an unwanted distraction that can slow down their progress with idle chat.
2. Or they are hiding something they don't want you to see. They are uncomfortable showing or are embarrassed by the fact that they have to resort to unsightly, violent or unethical training styles.
If your trainer asks for privacy, don't be afraid to ask them why. It's your horse, isn't it? You're paying for the training, aren't you? Whenever I train for clients I invite them to join every session. If I have to be firm in a safety situation, I explain it. I use it as a teaching tool for increasing the client's leadership when I'm not there to support them in the future.
If your trainer expresses shyness or introversion or a lack of confidence with an audience for fear of losing focus and being unsafe, then tell them to slow down get over it. You should be considerate of not interrupting them during important moments, but remember you're supposed to be paying a professional, not an amateur. Never forget, it's your horse, your money, your investment, your future. Be the leader your horse deserves. Make sure your horse doesn't get put in an abusive situation just because the trainer wants privacy.
I know I sound a little harsh on the topic, but I'm serious about how horses are treated and how customers are treated. I give full transparency. You should ask for nothing less... unless you're attending a magic show. But horsemanship isn't magic. It's easily definable with sequential stepping stones of progress. I can show you every step that masters follow. I have five ground steps and thirteen riding steps for mastering the foundation riding and riding preparation. If you want to learn them, consider joining my mastery group.
It's free to look and I'll even give you a free strategy session to help you out right where you are: https://masteryhorsemanship.com/pages/horse-mastery-group
Testimony from Patty in Florida about he horse Mastery Group:
"So I have to give a HUGE SHOUT OUT TO MY COACH/MENTOR
Don Jessop Mastery Horsemanship!! If I can train ride a 3YR old mustang at the age of 60 it’s because of Dons guidance. If you have a horse you are having issues with OR a young horse that is ready to start..... reach out to Don. He truly has the BEST program out there. Find him here on FB. You can pm him also!! I’ve been a student of Dons for a while now and I will ALWAYS be his student. His program is SUPER simple to follow and we do LIVE calls weekly!!"