A SPORT has an opposition, a common goal, and a score.
Dance, martial arts, etc. are considered performing arts, not sports.
I know competitive dance has recently come into play, but ORIGINALLY dance was an art, and purely for the performance. It was not a competition. I also don't think there is any way to truly judge a dance. Different people react in different ways, and it's so subjective. In soccer a goal is a goal, no question about it, but in dance one judge may give you a lousy mark and the other may give you darn near perfect.
Dance may not be a 'sport' in the technical sense, but ballet dancers are still athletes.
It's just a definition thing, that's all.