I started teaching classes a few years ago, and had no idea what I was getting into! As a mostly self-taught potter myself I never realized how much I just did things, without thinking about them...or even knowing I was doing them, until I started teaching. My throwing has improved a lot since i started, from having to trouble shoot beginner problems, to having to be so aware of every movement I make at the wheel so I can explain what I'm doing to my students effectively...it's crazy. I think it's a great learning opportunity for any potter to teach someone how to throw, even just the basics. It has made me appreciate teachers so much more, I am just in awe of people who do it for a living. Hats off to anyone that does, you all are the best!
I very much second (third, fourth!) the idea of throwing with your eyes closed/blindfolded. My grandma taught me to throw and that was standard, any time I was having troubles "Close your eyes and feel the clay! Staring at it isn't going to fix anything!"