Many trainers can ride a horse and teach that animal to perform well, safely and correctly all the time. Many times however, that same person cannot watch a rider and tell what they are doing with their bodies to make a horse perform a certain way - even though the trainer is doing the same things when the ride. It is very important to observe a few classes before making a commitment about lessons. If the instructor will not allow you to come and observe a few classes before making a decision, consider another facility. It is the opinion of the author that if observers are not welcome, the attitude of the instructor may not be open and willing to share knowledge.
Many instructors refuse to allow parents and other students to observe the lessons.
A few instructors have said to the author in the past that they did not want to give any information away for free, so no one was allowed to observe the lessons. Anyone seriously involved in instructing riders will be able to tell you that it takes years of instruction for a person to reach a high level of competence. If a person stands and observes a few lessons, what they hear might reinforce what they have already learned but it will not create an accomplished rider. Nor is listening to the instructor give a lesson going to enable the person who is listening to get on a horse and perform those skills. The more the instructor is willing shape knowledge the better off everyone involved will be.