I think she also wants to show you what a well trained horse is suppose to be like. She wants to set goals for you.
I wouldn't complain. You are getting to see what a really good horse is like to ride
Knowing her horse as she does she knows she can call out instructions that will work for both of you.
On your horse niether you or the horse will know what she is talking about.
Enjoy the free ride on a well trained horse.
If you don't like the horse then maybe reassess the trainer.
I always assess someone by the work they have done or in this case by how well the horse is trained. Good horse, good trainer.
It depends on what you know/can/goals are. If you are a great rider and take lessons to teach something your horse, then I don't quite understand it. But if you are green rider or have no experience in particular discipline it perfectly makes sense, because YOU have to learn first before teaching your horse. That's what I do now: take jumping lessons on solid trained horses before starting to teach my own horse to jump.