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's not anti-intellectual to require someone back up their statements from authority, it's science.
Anti-intellectualism is when people start making ridiculous statements like "classical literature is boring and irrelevant" and "college is a waste of time" (rather than merely overpriced).