Green Day is not a metal band. They are considered punk.
They aren't that bad actually. Some of their songs (which are mentioned in the first comment) are bad. I agree.
But some of their songs are decent. Such as "Wake me up when September ends" which is about lead singer Billie Joe Armstrong's father's passing. Or "21 guns" which is a reference to the 21 gun solute done for fallen soldiers. It's an anti-war song.
So they are decently okay for teens to listen to as long as moderate what songs they are listening to and you check the lyrics first hand. I recommend you do so for all the music your children listen to.