At one point in my private, the teacher said he wanted to see my "natural" walk (not when dancing tango). After I walked normally (for me), that's what he said was unnatural, and tried to explain to me why.
But then, that's my pet peeve with so many teachers... they don't take into account the typically unconditioned, middle-aged (or older), desk jockey bodies that so many social dancers come into tango with. (not talking of YOU DC). I've personally found this to be more true of young show dancers. They just can't relate. Although I have had dancers who perform work well with my body, and some older teachers who seemed more "social dance" oriented, oblivious.
All this just proves that teaching is a different skill than dancing.