Aha! My research has found the answer!
One guy wanted 4chan/7chan/420chan/whatever to help hack/raid the girl he was stalking. Anonymous replied "We are not your personal army. GTFO."
He could have just shut up there and sought help for his stalker issues. And his weight problem and acne, for that matter. Instead he complained at Anonymous, so they instead hacked him, putting his details up for all to see, putting gay porn on his MySpace etc.
He then decided to make a big issue about it, and tried reporting them to the FBI, who didn't particularly care. He also tried hacking the chans, getting them shut down, causing general trouble. It more or less failed (though one of the chans did remove their /i/nvasions board. 4chan didn't have one, so I guess it's one of the others), and they just gave him a harder time. Finally, he went to Fox News.
Well, the Fox News forums went down for a while, as Anonymous flooded the place with inane posts. I'm not sure if that "Taught them not to mess with Anonymous", or if it "proved them right", really. Also, a huge retaliatory strike is being planned against the guy who started it all, in the form of getting free fed-ex boxes mailed to him (in the region of several thousand, with a goal of a million). Childish, attention-grabbing, but not harmful at least. Much as I think he's a moron, I wouldn't wish harm on him and don't want to see the chans brought down as a result of people getting hurt.
They've done the fed-ex trick before. There was a racist podcaster who they had a real laugh with, and possibly others too.
This are a fact. I know because of my learnings.