Seeing I'm ill and spending my day in bed working on the biggest coaching challenge I've ever taken on I might as well share some musings on various teaching related subjects. Lots of waffle below, you've been warned.
In addition to the question in the title, there is another one: what do riding coaches need to deliver?

Creating the Academy project pushed me into reading a lot on various coaching methods, to watch others training and to listen to riders views on various coaches/instructors/trainers.

In my teens and the riding environment I grew up in, there was no proper dilemma. If you wanted a good coach, if you wanted to test how good you can be, you went to the best competition rider in your chosen discipline that you could (or couldn't) afford and you hoped he would have the time to squeeze your training in in between his own training sessions, competition schedule and producing young horses. There would be no time for questioning the methods or having your views on things. If you didn't like it, off you went.

It wouldn't have crossed your mind to go for a lesson to a girl/boy down the road, with new set of coaching certs who jumped in an odd class and managed an elementary test outing a few times a year.
I was no different. Many years later, however, I realised there is often much more to learn from those less obvious individuals. It's no secret that if you worked hard on understanding something you are in a much better position to explain to someone that very process.
Funnily enough, I learnt that very early from my brother. Robert is one year younger than me but was a clever child so we started school together. I loved all humanistic subjects and he was a maths little genius. Many a time I would ask him how he came up with some of our homework but his explanations were so vague (from 'I just guessed it' to 'well, they want you to do it that way but I found another, quicker, way and the results are the same') there were of no help to me. In fact, he occasionally failed some of his exams as he didn't use the formulas we needed to use (despite all his results being correct!). It took me hours to do what he did in 5 minutes and even when he tried he couldn't help me!

Horse riding doesn't seem that much different...If you teach you will most likely have some preferences as to what you teach. I personally often chose to teach on the flat. This is because, whilst jumping I learnt by feel, watching and being immersed in a show jumping world, the flatwork I needed to analyse and teach to myself.
If I have a rider with problems on the flat, I see a problem and almost immediately also "see" the things that need to change, things that need to improve and most importantly, a plan a,b,c pops into my head as to how to go about it.
Jumping is a different story. I see what's wrong but my first thought usually is 'I would want to sit on this and feel what's going on in this horse when it does x,y,z in front of/after/in between the jumps'.
The way I see it, every horse gives you feedback, in the very first second you sit on it. Riding on the flat, I am sometimes deaf to that feedback and go through what you might call 'trying to explore/investigate a horse' period. It can last 10 minutes or a few days...
A jumper on the other hand...the moment I point it at a jump I can "feel" the information I needed and that took me days to discover on the flat.
The "feel" is only the starting point though. Acting on it is what in my eyes at least, is what we are learning all our riding lives.

This is why the Educate Not Instruct is what I find very, very difficult part of my teaching. It's also the part I like the most - the explanation of how to and why act on different feels.
There is a lot of people out there with so called good eye who can tell you what to do to make things better. What I personally find the most challenging is to what to tell the rider so they 1) understand why I am saying what I'm saying 2) why this might be better 3) how will this change the horse 4) how to replicate this when I'm not around.
The latter, that ownership of knowledge is so important. I had some amazing lessons in the past and my horses went the best they ever did and yet I could never repeat that performance at home. Maybe it was just me lacking in skill but whenever I teach I hate sending riders away not knowing the How-To and the Why.

Another big one amongst riders is the feeling of confidence. In both themselves and the horses.
Totally understandable. However, riders don't like to be protected and told all the nice lies. They like the truth about their skills, their horse's ability and they like to know what they need to work on. The problem is, often the answers is LOTS...It's easy to lose your confidence when you're told how it is and how much talent your horse is, well, lacking.
So, to give accurate assessment and yet inspire the greatness - yet another teaching challenge.

There you go, a bit of random thoughts while I try not to think about the sore throat and the insanely running nose! Feel free to comment on your experiences with different trainers...