Using the kids/obesity thing in this case might look good on paper, but the hard reality is that not one single fat kid on the entire planet is into sports anyway. For no fat little plumper is going to belittle themselves in front of anyone, so the obesity slant just doesn't hold up.
You are obviously a man into sport yourself (and probably rightly so), and you ask what's wrong with anti-sport people. First off, it has nothing to do with anti anything; it's all to do with been forced-fed a constant barage of televised events and/or sporting events in the media in general. To get the bigger picture, first think of any particular thing that you yourself are not too interested in, then try to imaging how it feels when your television/media are forever ramming down your throat a constant and incessant diet of the stuff.
Try it and see what I mean. Tune your television or radio to a channel that you wouldn't ordinarily watch or listen to, then pretend that that particular channel is the only channel available to you, then force yourself to a constant dose of it. Of course, you will never get the true picture because, where you live, you do at least have the option to switch channels. And the hard truth is, no man will force themselves to do anything they don't want to do anyway, right?
Whereas, we in Blighty aren't offered the same freedom. The only option we have is to switch off the damn TV off altogether, for just about every single radio and TV station are puking-out the same old endless stream of so-called 'sport'. Sport should great, nothing wrong with sports at all... when its done properly. But by today's definition of the word, sport is anything but. It mostly concerns money and egos.