As any good music nerd, I have had several conversations with friends and colleagues about technique and general teaching. While this cannot intrigue anybody but a real dork, I need for you to bear with me and read on.
If you majored in music, like me, most of us had more than 1 private teacher throughout our entire musical journey. If you were lucky, all of your teachers were able to get their message across, were able to clearly explain their points, successfully demonstrate their point, and inspire you to become better. While these qualities seem like a common description of what a teacher should be, you must keep in mind that music education and technique has developed substantially over the last several decades. There is however, a lot of truth in what the article in the link outlines.
I have experienced/observed teachers who can explain their point without demonstrating on their instrument (for private lessons this is not my favorite, but sometimes logistics forces you to do it). A lot of hand signals, singing, and demonstrating on your arm occurs when you have to do this, but if explained correctly, the point can easily be made to the student.
There is also the incredibly gifted performer who demonstrates their points, plays musical passages and concertos for you, and entertains you with tales of Studies with their mentors. However, when the time comes to explain their points, they find it difficult to be clear and concise. Things come so naturally for performers that sometimes they find it difficult to explain and break down the process for somebody. Performers play, they aren't necessarily teachers.
I can go on for days if I gathered up all the different stories I've heard and mushed them together, but I'm not going to ask for that much of your time. The article in the link below goes through an artist's experience with different teachers and how he actually taught himself. At the end of the article there are 2 great links that I would highly recommend. If nothing else, follow the link for the incredible Premiere performance of the "Tzigane". Enjoy the article and the links.