Lyric discussion by Tunhizzle 

Cover art for Leave lyrics by Glen Hansard & Markéta Irglová

I actually think this song is really about after she leaves. What he's singing about now is how she hasn't left his mind yet. In the first verse it deals a lot in the past tense, showing how it could have possibly have happened a while ago. What he is telling to leave is his memory of her, because no matter how far away she is, she is always on his mind. He wants her out of his head so he tells her to leave. If you look at it that way, the outbursts of emotion toward the end are completely justified and really makes you feel his pain. I think that initially telling someone to leave could not cause that kind of emotion so I believe its his way to cope with the memory of her.

My Interpretation