I think the internet is, for those who can take it in, very humbling. The anti-intellectuals are the people who react badly to this overwhelming sense of one's own smallness.
In 1900, colleges decided what it was important for an upper-middle-class person to know. One set of writers and texts was in the canon; the rest were not. Sometimes the selection was based on quality but it was often political as well. It wasn't actually possible to have "all knowledge" but one could get all the "important" knowledge in a few years of study. Any thinking person in 2011 realizes that this is no longer true (if it ever was). There's a million times more genuinely valuable knowledge out there than anyone can take in in a human life. Also, the authorities once trusted to decide what was important have been disrobed by technology; the increased power of technology has allowed us to discern that they aren't much smarter than the rest of us.
Anyway, the result is that a lot of people get really insecure and overwhelmed when they realize how much they know nothing about, and there's a tendency among some people, as a defense mechanism, simply to declare large sectors of knowledge useless, unimportant, or outmoded.
It's not just the less intelligent who have this attitude either. I've heard an esteemed computer scientist (someone with a name, but I'll withhold it here) argue that the only useful literature is science fiction because everything else is "just the seven deadly sins, over and over again".
It isn't that the elites are about as smart as the rest of us, it's that they were usually found to have their own agenda, regardless of the ideals they espoused. Just another case of someone telling you "it's for your own good", when really it was for theirs. "Intellectuals" are the ones who are reacting badly, when their "authority" is challenged.
It's not anti-intellectual to require someone back up their statements from authority, it's science.