Trying to explain what is and what is not a sport is not easy to do.  A sport is defined as an activity involving physical exertion and skill in which an individual or team competes against another or others for entertainment.  I think that in order for something to be considered a sport there needs to be some form of athleticism involved and it needs to be competitive.  Also it needs to be entertaining to watch. 
One activity that is debated over whether it is a sport or not is cheerleading.  Cheerleading that you would see at a football or basketball game should not be considered a sport, it should just be considered an activity because there is not competition or goal involved, it is just a group of people cheering for a team.  The cheerleading that you see at competitions should be considered a sport.  It requires athleticism and multiple teams compete against each other. 
Another shady activity would be ping pong.  Although it is not really looked at as a sport technically it should be.  It requires some athleticism and there are two people competing against each other to achieve a goal.  It is also in the Olympics which means it is viewed as a sport by many countries even if most Americans only view it as an activity.