"I cannot teach anybody anything.
I can only make them think."
Back in the day Joseph Pilates taught just one person at a time. He taught them the exercises they needed for their body. He mentored them. He made custom workouts to allow his clients more success through movement. Some had special needs or injuries. They were given a program design on the equipment to accommodate this and Matwork as their homework.
Sadly at this day in age most people experience Pilates in a group environment. Why pay someone up to 10x the amount for a private compared to a group session? For the exact same reason Joe would teach you one-on-one.
Learning Pilates is a way to discover how your body moves and learn to make it more efficient and balanced. You may think you are doing a movement correctly. You may be able to fudge your way into a Teaser but the real point of Pilates is to learn the best movement pattern for your body to be able to do that Teaser effortlessly. That's where the beauty, grace and flow of the system come from.
Let me prove my point. Right now I want you to get up from your computer or phone and stand up.
Cross one foot over the other and without using you hands descend to the floor with ease. Now come back up the same way you went down.
How did that go? Not easy is it? If you had someone helping and coaching you through that basic movement of survival it would be easier and I argue you would find more success in your movement patterns.
As Albert Einstein said, "Any fool can know. The point is to understand." Don't feel intimidated by a private. Use it as a chance to learn and grow. A time to have your questions addressed and to peel back a layer of your onion.