A sport is defined as an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment.
Dance is a beautiful thing that many children get involved in from a young age to learn different values and morals that are used all throughout life, and is also an activity that people can get involved in to keep fit and healthy. So to me, for someone to say that dancing is not a sport is completely and utterly ridiculous! It is appalling that someone can have the audacity to say that to move and contort one's body, balance on one leg whilst rapidly turning on the spot, flipping through the air and defying the laws of physics does not fit the criteria of a 'sport', but rather a hobby or interest.
The thing that makes me laugh is that these people are the ones who can't themselves do a handstand, let alone the amazing feats that a dancer can manage to do.
I do not believe dancing is considered a sport. My reasoning is that most sports contain a specific goal; such as getting the ball into the basket in basketball, getting a goal in soccer, capturing the king in chess, etc. Now, while I do believe dancing is a form of physical activity and exercise, I would not consider it a sport. For example, if you are performing in a ballet dance there isn't a goal in terms of winning or losing, the only win/lose condition is if some people enjoy the routine and some people didn't, but if you are playing another sport such as soccer, you don't win based on how people enjoyed your performance, you win based on how well you played.
I understand your argument, however dancing does have an aim and is, on occasion, competitive. Although it is often perceived that dancing is merely a form of art and is conducted only for people's enjoyment, in many circumstances dancing is competitive and competitions are held all across the world, from amateur levels to national events. It is quite intense, and if you have ever heard of the show Dance Moms you would know exactly what I mean.