Basketball players often dance before games to pump up the team, people go out to clubs to dance, to Salsa, Tango, etc. People record their dancing on youtube as a performance. Yet people rarely dance at home. Rarely simply dance. It definitely does happen, everyone does it every so often, but it's rare. Moreover, rarely have I seen other people dance at home, even if they sometimes dance when they're alone.
Singing - people constantly sing when they're alone and in very small crowds. Playing an instrument - definitely. What is different about dancing? What about dancing makes us need a crowd around us?
What makes dancing a public activity?