Paul Zindel likely used animal imagery because it is something that most of his readers would be familiar with. Giving animals human characteristics is a very common form of personification. It's been happening in literature for as long as people have been writing. It's also pretty much what Disney has made an entire enterprise out of (Lion King, The Fox and the Hound, Oliver and Company, The Aristocats, etc.).
In addition to readers being familiar with written personification, readers are also familiar with seeing their own traits and behaviors in real animals. It's a big part of what makes going to the zoo so appealing. People go to the monkey exhibits and witness the monkeys doing things that people actually do. It's the same with even species that are not closely linked to humans. Watching lions lounge around in the shade always looks so darn appealing. It's what I want to do on my Sunday afternoons anyway.
That's probably why Zindel made the zoo such a central focus of the book. The monkeys at the zoo are in cages. That makes total sense, but Lorraine herself sees the connection between the monkeys' actual cage and the metaphorical cages that she, John, and Mr. Pignati all struggle within. Another time, the three main characters witness three monkeys all hugging each other and acting crazy. Lorraine sees herself, John, and Mr. Pignati in that moment as she recalls the three of them all rollerskating together. She thinks,
"We must have looked just like three monkeys. The Pigman, John, and me—three funny little monkeys."
That kind of logic is familiar to Zindel's readers, so it makes perfect sense that he uses it in his book. It lets him effectively make his points without taxing the reader too much with some obscure and difficult bit of imagery.