Lyric discussion by andmcg1 

Cover art for I've Got A Match lyrics by They Might Be Giants

It's hard to tell what it's about, it really needs more lyrics. :) It sounds like to me that it is about two people, let's call them him and her. She wants to be with him but he is either not interest/disgusted by her, or by the whole concept of love.

But I don't know where this line fits into that theory "Beat up the cat if you need someone else on the mat"