Lyric discussion by Comebakatz 

Cover art for Sundays lyrics by Counting Crows

Sounds to me like it is a song about a girl leaving him. She claims that she can live without him, but he realizes that he can't live without her. Even though he didn't have a sexual relationship with her he didn't need it, he was in love. She left or threatened to and said walking away would be easy. He knows that his 'moon will explode' without her. I think "I don't believe in Sundays" is a way of saying the he won't make it to the end of the week without her. Not believing in anything make be him admitting that love doesn't exist.