Lyric discussion by onset 

Cover art for As I Sat Sadly by Her Side lyrics by Nick Cave and the Bad Seeds

The narrator, not the woman is sick - depressed, and his lover is trying to reason with him, to bring him out of his depression.

Their world-views are contrasted in snapshot - she sees variety and purpose and beauty in the world, he sees pain and greed and meaningless suffering.

She gets upset and lashes out at him for letting himself be crushed by the weight of the world and wasting away his own life worrying about things beyond his control.

Finally she turns away in tears, and the narrator can't help taking perverse satisfaction in having provoked her and and dragged her into the mire with him.

This is my take on it at least. I know this dynamic all too well, it's what happens in a relationship when one party is depressed but indulginging in it and compelled to bring down his partner. The irony this song is about is how the one who thinks he is so sensitive can yet be so cruel and selfish.

I think the third verse, where she lashes out at him, is the crux of the song, and it's the lesson I take from it, every time I listen to it.