Companionship
The main theme running through the story is the idea that pets can be lifelong friends and indeed, family, in one’s life. Seuss himself was very fond of pets and owned a dog, named Theodore Seuss Geisel. He kept the dog for the entirety of his life, and when he passed, he left it in the care of his stepdaughter. Thus, he seems to suggest that pets are family for life.
Imagination of children
Both Jay and Kay are young children who are intrigued by everything they see. They are curious to explore every pet on offer and refuse to compromise on the scale of their search. Indeed, they even go on to make up their own pets, such as a Yent, such is their vivid imagination!
Leadership
A background theme in the story is one of taking responsibility and making a decision. Both Kay and jay let their imagination run mild and ignore their father’s instruction of choosing only one pet, for most of the story. However, eventually, Jay makes a decision to choose the one pet, thus portraying him as a level-headed and responsible young man.