Green Day isn't even a rock band...it's funny how they are classified as rock. Punk is terrible, the whole genre is just crap...it takes the musical ability and vocals of 4 year olds to make it.
Last time I checked punk is a subgenre with in the rock spectrum. Just like jazz has several different classes (Swing, Cool, Be-Bop, Hard Bop, Fusion, etc.) so does rock (Punk, Alternative, Lo-Fi, AOR, Heavy Metal, Grunge, etc.).
Listen to American Idiot in its entirety and then tell me if it was written by 4 year olds.