Why did Howard Dean's scream destroy his campaign?

[I spent the winter writing songs about getting better]

It didn't. In the run up to Iowa, Dean had opened up a pretty solid and significant lead, not only in Iowa but getting ~40% in the national polls in a very crowded field. However as Iowa approached evidence indicated that he might be slipping there, and Kerry (who's campaign had previously collapsed and was being written off) and Edwards (who was always seen as a huge longshot) were unexpectedly gaining steam in the final weeks. So while speculation opened that Dean could lose Iowa, few expected him to lose as badly as he did coming in third. "The scream" then happened, but it wasn't really a big deal, Kerry was effectively anointed as the frontrunner, embraced by the establishment, and the damage to Dean also took out his lead in New Hampshire. His campaign effectively collapsed after that.

An interesting theory is that it actually hurt Edwards more than Dean, since the media attention on it caused less attention to Edwards' 2nd place finish.