The internet isn't a human right, no, but in these days, its becoming a sort of hurtle that organizations and businesses would need to overcome, as education can be a financial boundary keeping the wealthy and the poor separated.
Education is also considered by many as a right, but if it weren't on its own, it is a manifestation of the concept of the "Pursuit of Happiness" being a human right.
Yes, it would likely throw the 'Net into a state of chaos for a while, but in the long run, it could be a beautiful thing. (well, as beautiful as the internet can get, anyway)
Really, though, with the internet being such a huge part of our society, for the sake of everyone, in the wealthy countries and the poor, I hope the internet becomes categorized as a human right.
I mean, remember what's happening in Canada? What happens when a handful of superpower companies dictate the sites and content of the internet as a whole?
You know that unless something seriously changes, it is going to happen.