I also think it’s worth keeping in mind that by and large, someone that makes it through to being a good coach or trainer is going to inevitably be someone that was always a good rider compared to their peers, and that has natural athletic ability. Especially for trainers that jump, it’s not uncommon for them to also love other high speed, high skill, high risk sports (like downhill skiing or kayaking).
A certain percentage of young riders are going to be in that category, natural athletes with balance and a taste for risk. But especially in their early teens, girls can have all sorts of fears and anxieties that might make them less able to fully exploit their natural athleticism. Girls even today get so many warnings against risk taking in every other aspect of their lives, that it is not perhaps surprising that by 13 they may start to pull back a bit.
However, it’s also true that many of us come to riding horses as the only high risk, high speed, high skills, sport we have ever done or ever will do, or want to do. Many people ride because they love horses, and have to develop the skills and the taste for calculated risk over time. Many, maybe most, adult re-riders or beginners would never dream of taking up downhill skiing at the age of 45, but they have a great drive to learn to ride.
I think it is hard for coaches who are natural athletes to always know what to do with the riders who are not. Simple things like proprioception: does the rider actually know where here hands and feet are in space? Or natural balance. Or fitness and stamina. Or problems with body alignment that make it really hard to get a correct seat or leg.
For me, the comparison is teaching college writing. I have to step down and really think about how to communicate basic skills to people who are not “natural writers” but can become quite competent with some focused instruction.
Anyhow, I’ve been in salsa fit classes where the instructor tells the class to hold the one pound weights out ahead at shoulder height, and seen arms go flying off in every direction, up down and sideways. That tells me that a large part of the population probably has given no thought at all to where their body is, and if you had someone like that in a riding lesson, they might well mix up right and left, inside and outside, up and down.
If it’s an adult doing it, people tend to say well, she’s just a klutz, let’s go slower. But if it’s a kid doing it, people tend to say, she’s not listening or she’s not trying. Or she’s doing it on purpose because she doesn’t want it enough. Or whatever.
In general, I think kids need to be treated with more respect. But that doesn’t mean cooing “good job” over every little try. As a kid I was ahead of the curve on art (which I did not pursue to adult professional standards) and writing/ reading (which I did pursue to adult professional standards). I often thought adults were extremely stupid because they would praise efforts that I knew were mediocre, and had absolutely no suggestions for how to improve. I wanted my art to be super realistic, and everyone cooed over it when I knew it wasn’t up to my own standards 
I did not feel the adults were treating me with respect, because they were not able to distinguish between my best efforts and my mediocre ones, and they did not acknowledge my own desires to improve.
On the other hand, phys ed class was a hell hole.
The end result was that I became very self-directed on the things that mattered to me (writing and riding).
Interestingly, I did not consider riding a “sport” as a kid, and neither did the grownups around me. It was a hobby or an activity, and I came to think of it as an art. I was well into my 40s, listening to some radio program in the car that extolled the value of sports for teen girls and scoffing silently: well, I got all that (discipline, fitness, focus, responsilbity, an interest outside myself) from riding. I certainly would never have got that from a sport. That was when I finally went: oh, right. Riding is a sport. 
Nowadays you can get credit for gym class in some school districts if you take riding lessons.