I don't dance, in public or in private. In a similar context I don't sing either. I feel no urge to, and derive no enjoyment from it.
As I view those activities as outward expressions of the self, I'd never feel comfortable doing that in front of other people. (I might feel a tad better doing a 'structured' dance like ball-room dancing, though.) Doing that in private is sort of pointless for me, because I know how I feel at all times, and don't really need to express it back at myself.
I don't reckon I'm missing out on all self-expression though, because I'm really keen on playing the guitar. If it's indeed my voice speaking through the instrument, then it comes with badass amplifiers.