As a dancer, I think I am qualified to say that dance is not a sport. But no, it’s not because we don’t work as hard as athletes and no, it’s not because we don’t compete, and it’s definitely not because dance isn’t mentally and physically demanding like a sport.
Dance can be extremely competitive, and some may even argue that dance requires more athletic ability than other sports. Some moves require features physiologically unnatural to the body, such as “turnout,” which is a rotation of your leg so that your knees turn outwards away from the center of the body.
Sports are governed by a strict set of guidelines. There is no concrete scoring in dance because it is too subjective for an official scoring system that everyone will agree upon. Although you may be able to score aspects like timing and formations, there is always a factor of subjectivity. One judge might look for synchronization and another for musicality and expression.
Although technique is a big part of dance, how well a dancer communicates with an audience is what turns a good routine into a beautiful routine that can bring an audience to tears, which is why dance is more of an art than it is a sport.
Like musical performances, dance routines are rehearsed for hours, until it becomes muscle memory. The goal of a dancer is to make it seem as if the routine is effortless. The performance should be expressive and artistic. Yet dance is not exclusively an art.
So calling dance an art form is not an insult, but calling it a sport would not be a compliment. They are two separate categories and neither is necessarily a better fit than the other.