Lyric discussion by Yasuko 

Cover art for Speak Slow lyrics by Tegan and Sara

This song is just about someone not letting their love go and then realizing that they want it back just because.

when your love lets you go you only want love more even when love's not what you were looking for

They probably didn't want love in that relationship but they want the security and comfort OF a relationship. It doesn't matter what they're looking for, they just want what they had back.