Hi Je Yeon,
You have raised a fantastic, straight to the point, question but unfortuantely I believe the answer is very ambiguous.
In my opinion I believe that dancing can't be classified as either a sport or an art but is rather defined by each person that experiences it. Basically what I am saying is dancing is neither sport nor art but is rather whatever the dancer or spectator defines it as.
In my opinion dancing is an art and not a sport. I can't argue against the fact that it is not a sport, but I can say that the reasons why one would classify dancing as a sport can also be the criteria that classify dance as an art.
Firstly dance is an expression. It is physical movement that conveys emotions, story's and character. There is a point to each movement (we don't just do something for no reason, it has meening) and there are special techniques that are used to be able to convey and communicate our story to those that watch us. This is similar to visual arts where artists use special techniques (ie brush technique, texture, etc) to help create a story that people can interpret. Art is a form of creation, artists create meening and definition by touching peoples emotions. Dancing involves physical movement to create story's which is a characteristic of art.
People tend to argue the fact that when one performs dancing in competition it immediately turns in to sport. I will not criticise this opinion and nor shall I try to disprove it but I will provide with my reasoning as to why competition dancing for me is still defined as art. Consider an art exhibition in an art gallery. Judges have certain criteria that they use to choose a winner. In almost all cases the winner is the artwork that has the greatest impact on the judges (touches their emotions, greatest depth, etc). Each artwork is judged on its own merrits. Rather than competing against eachother, each artwork presents what it has to offer- the story hidden in it, the emotions conveyed the technical expertise. Same in dancing. I do not believe that dancers compete against one another. I do not view it as competition but I do believe that it is an exhibition with each couple having their individual strong points. These strong points are the different characteristics of their art. The winner will be the one who has the greatest impact on the spectators and judges. It is not saying that they are better than the others, but is rather saying that what that artwork has to offer has the greatest impact on people.
Finally someone argued that dancers are athletes because they have to keep their body in tip top shape. I argue that dancers are not required to keep their body in great shape, they choose to. One can still create if they are out of shape but will that have such a strong impact on people? If one finds your artwork offensive then they will not try to interpret it nor find the many meanings that are hidden in it.