Does the world just drive you crazy some times? And not in that fun Britney Spears sorta way? The speaker of "America" is definitely not having as much fun as Brit is in that song. In fact, he's so bothered by the problems that he sees in his country that he struggles with his own hold on sanity. And in a world of atom bombs and unjust persecutions, what does it mean to be sane anyway? Maybe all it takes to be labeled insane is to be sane in an insane world. That's just one of the big picture questions our speaker is dealing with.
The speaker's admission of his mental trouble undermines the validity of his criticisms. He's nuts, so how can he expect us to take him seriously?
By acknowledging his own mental issues, the speaker makes himself a credible critic of his country.