For the younger set, cheerleading would have to be considered more of a sport because it gets sanctioned by high school associations and is supported by booster clubs and fund-raisers and such. That is a different way of looking at it, but it addresses the public perception, I guess. But ballroom dancing may someday be embraced as an Olympic event and its DanceSport competitions are already world-renowned. They both take a lot of time and effort, with cheerleading probably being a little tougher on the participants' knees and backs.
From a man's standpoint, they are so different, that the argument, while interesting, is akin to a couple of guys arguing whether poker or golf is more of a sport because both include lots of wagering and both are on TV a lot.