"Those who can, do. Those who can't, coach."
For example, Butch Harmon, one of Tiger Wood's swing coaches. I have no doubt he can play the game at a high level, but look at what he can do for somebody with a gift! His understanding is such that he can analyze and correct someone of the highest level. Much higher than he himself can play at.
How about National Team coaches from various nations. If they could ski as well as their athletes, they would be racing themsleves- not standing on the sidelines! They too have a knack for getting their athletes to perform at a level higher than their own performance.
I think skiing is somewhat unique in this regard. To teach/coach well, it takes the ability to understand the information, to be able to break it down in a useable form, and to be able to demonstrate what the outcome should appear as (among other things). What I found in my years teaching/ coaching, was that the better I understood the mechanics, the better I was personally able to ski! Oft times, the visual model was the athlete I was coaching! The better I skied, the more I could do for my athletes. It became an ascending spiral of improvement.
Coaching at an elite level is a very special relationship between the skier and coach, involving trust, respect, psychology, and knowledge. Teaching recreational skiers demands some of the same qualities, but is not usually developed to the same degree as the long term relationship of an athlete/coach.
It also requires that the student be receptive to feedback offered by the coach, and an honest attempt to make the change (oness of compliability). Some people do not have a high capability to change. They have a natural resistance to change, even if they identify it as a positive thing. This partly, but not completely, relates back to the trust issue with the coach/teacher.
In extreme cases where a 'rebuild' of a skier is needed (where fundamentals are grossly deficient), then it is taken to a level where the skier's entire belief system needs to be rebuilt before any change can possibly take place. For this 'rebuild' to be successful, the afore mentioned qualities need to be exercised at near a coach /athlete level.