The correct version is: "Those who can, do. Those who can't, work for the government." Or have you forgotten these are all gov't employed teachers; and do you think most private teachers are this incompetent (private school teachers are an in between case, how bad they are depends partly on state requirements).
I've never liked that phrase, even though I recognise it's true most of the time in the public school system. But the idea behind it, that teaching is a last resort job for losers who can't do anything else, is very damaging to society, IMO.
Also, the first thought that comes to my head (after all the bad teachers I've had anyways... ) is that Feynman loved to teach. And I'm pretty sure he could "do".
Those who can't do, can't teach either.
Around here we have an extension. "Those who can, do. Those who can't do, teach. Those who can't teach, administrate. Those who can't administrate, teach gym. "
It's a phrase true mostly in the public school system. Doesn't hold so much for universities or other educational institutions.
My understanding is that the phrase refers to the fact that athletes and others go into coaching/teaching when they can no longer do the sport (etc) because they are too old. It was not intended to suggest that teaching is a last resort job for losers who can't do anything else. It means when the body can no longer stand up to the rigors of professional dance, professional sports, or anything else that is a young person's game, age and experience mean they still have something of value to offer.