Animals probably represent Jerry's baser nature. That is, animals act, sometimes brutually and sometimes seemingly without cause of attack. In a zoo, those animals also suffer isolation.
Jerry's life is not going well. He lives in a tenement building on the "bad" West side of town. He is also caged like an animal there; the room he stays in is not even a whole room, but a single room divided by a large piece of beaverboard.
Emotionally, Jerry wants to ask questions, evalutae and manipulate Peter's answers, but he does not want to be asked or reveal anything himself. He uses Peter's answers against him, making the slightest thing questionable. For example, when Peter reveals that he has daughters, Jerry quickly makes him feel badly for not having sons.