In Greek mythology, the Minotaur was a creature with the body of a man and the head of a bull. This surreal music-hall parody is sung from the point of view of the mythical beast. The Incredible String Band's Mike Williamson recalled to Mojo in 2017:
"The Minotaur's Song was inspired by Gilbert & Sullivan and it had a humorous quality, but it was about the war machine. The world was less troubling then. It was easier to be humorous about things like that."
Kacey Musgraves originally offered "Follow Your Arrow" to her friend Katy Perry. However, Perry thought Musgraves should record the song herself as it seemed, "like something that you would totally say."