Well, they can't have "nothing" in common if you both don't believe in the existence of a god. You must necessarily share at least that much in common, if you both qualify as atheists. Also, I think it has to be more than just biblical, because that suggests Christianity only. I'd also wish to reject the concept of god for all other religions. If atheism is simply anti-Christianity, the term is not broad enough for my likes.
And I think your sentiment helps support the use for "atheism". You wish to define those who do believe as idiots. Thus the atheism label distinguishes you from that crowd.
And I think your sentiment helps support the use for "atheism". You wish to define those who do believe as idiots. Thus the atheism label distinguishes you from that crowd.