Lyric discussion by that one girl 

Cover art for Blood on Our Hands lyrics by Death from Above 1979

In the first verse, he's trying to avoid her, and he's hurting her with words (because when you bleed, you hurt). They've been avoiding the bedroom, obviously, from them falling out or they're sleeping around with other people. The guy has done more than one bad thing, and the woman is obviously very hurt.

Second verse, the woman is hurting other people, by screwing them over and the guy just wants her out of his life.

It seems that the guy wants to get back together with the girl, even after all the bad shit they've done. Anyway, I love all their songs, but this is my favorite as of current.