The song is describing the typical young, idealistic person who is always protesting social and political injustice. The angry young man, believing that he knows how the world should be run, spends his days making up radical plans to root out these injustices. However, as can be seen from history, these changes are rarely implemented, if at all. As a result, life goes on no matter who is wrong or right. The angry young man stays inside concocting his plans to change the world, and only gets angrier when nothing happens. As a result, he spends his days being angry at the world for not being idealistic and perfect, and ends up only torturing himself in the end. Basically, Billy Joel is trying to tell young, idealistic people that the world is never going to be perfect and you shouldn't obsess over trying to make it that way. Instead, just learn to live with it and don't get angry because the world isn't how you like it.