Sports are typically athletic activities that require skill, strength, stamina, and physicality. Most sports involve an element of competition against another team; sometimes the teams interact with each other; like in football, baseball, or basketball, the teams try to score against each other. In other sports, the competition comes from individuals or teams who compete to deliver the most optimal performance of the challenge, like who can run the fastest sprint, or swim the quickest relay, or perform the most technically accurate dive.
Competitive dancing has many elements of the aforementioned sports. It requires skill, strength, stamina, and physicality. Dancers' bodies have to be in extremely good shape to perform their choreography and often require years of training to reach competition level. Competitive dancing also involves competition between teams, in which they are scored on the basis of their ability to deliver the most technically challenging, synchronized, and accurate routine. In that aspect, competitive dancing is really not that different from diving or gymnastics. Based on these criteria, competitive dancing could definitely be considered a sport.