Sugar and Oil is written from the point of view of a man being left by his lover, with whom he seems to have nothing in common.

She’s a vegetarian, she is in PETA
Concerned about the ethical treatment of animals
I wear leather and I’m a meat eater
But we both love to dance to the Fine Young Cannibals

In this tenuous and coercive relationship, simply liking the same music isn’t enough to keep these opposites attracting. 

Stylistically I was certainly influenced by The Coaster's "Young Blood" and other songs of that genre.