mblase has written a good, factual, writeup, but one i feel lacking balance.
First, while same-sex competitive dancing is verboten, same-sex social dancing is taught (and enjoyed), both for those of whose chosen life partners are same-sex and for those (like myself) who feel the need to be able to dance either way.
Secondly, DanceSport and modern ballroom dancing place a very heavy emphasis on competitions. This is partly to remove the focus from the social aspects and make it accessible to a younger crowd (or agreeable to a young crowd's parents as the case my be), but it leads, in my opinion, to a dancing environment in which winning is the only goal. Some people thrive in such environments, some people don't. Whether or not it's a healthy environment for teenage kids to be spending all their after-school hours in is left as an exercise for the reader.
I dance ballroom and recently overheard one of the female competition dancers say to another of a third
Yeah, now she's done the nationals she's putting on weight to see if she can menstruate.
If you're an adult thinking of learning to dance, I'd suggest trying a more socially oriented form of dance. If you're thinking about it for your kids, I'd pick ballet over ballroom/DanceSport since while there's still the same pressure to have the perfect body, in ballet you don't have a 1:1 relationship with a dance partner but rather a group or team mindset.
Having said all that the DanceSport can be cool to watch, especially if you have haven't lost your ability to enjoy watching dance by spending too many years over-analyzing it. If I had a TV I'd probably watch it at the Olympics