I found this old essay I wrote about this play my senior year of college. it's pretty fantastic. I got to read it out loud in front of the class. SPOILERS
The Zoo Story is a play about two seemingly opposite men, Peter and Jerry, conversing in Central Park about their family and home-life. Jerry tells a long, rambled story about a conflict between he and his landlady's dog that seems to have little significance to anything. Peter and Jerry's encounter begins rather comically, but ends in shocking, sudden violence. After Peter accidently kills Jerry, the conflict between Jerry and the dog suddenly symbolizes Jerry's conflict with his own existence. Jerry dies in order to feel an un-compromised, active emotion from another person (or thing).
In the end, Jerry's desire to be killed in anger is a response to a struggle he seems to have with himself and those around him. It suddenly becomes clear, after he is killed, why Jerry told "the story of Jerry and the Dog". In the story, Jerry confesses sadness and humility that he and the dog no longer fight with each other, that instead they have "attained a compromise" where they "neither love nor hurt because [they] do not try to reach each other" (Albee 20). He is humiliated because both he and the dog have given up; they merely "regard each other with a mixture of sadness and suspicion" and "feign indifference" (20). When Peter decides to leave the park and go back to his home, one gets the sense that if Jerry had let him leave, then their relationship would have ended just like that of he and the dog, that of sadness and suspicion, where neither is loved nor hurt by the other. However, Jerry sacrifices himself in order to avoid such a compromise, devoid of any active emotion.
"The story of Jerry and the Dog" alludes to Jerry's own struggles with humanity itself. We learn details of his troubled upbringing, his non-existent parents, his confused sexuality, all of which give us the impression that he is a man tortured by life's ambiguities and ambivalence. He says "a person has to have some way of dealing with SOMETHING...if not with people" (19). Because of his unhappiness and detachment from other people, Jerry expresses the need for connection, which can come from anything, everything from pornographic playing cards, to a street corner, to a mirror ("that's one of the last steps"). Jerry provokes the confrontation with Peter that ultimately ends in his own death, because he wants to be reassured that resistance to a compromise of ambivalence is possible.
One could say that by "voluntarily" dying, Jerry has given up on life, that he no longer wants to live. However, the reason for Jerry's sadness and humility is because he is unable to find anyone, or thing, which is willing to be loved or hurt by him, or vice versa. The ambivalence of emotions is what depresses him the most. By allowing himself to be hurt, he is able to find reassurance that, even though he dies in process, he is able to connect with someone on an emotional level, he feels their emotion. As he lays dying, he reassures Peter that he is not a "vegetable" but rather, he is an "animal" (27). He is pleased to see that Peter has not given in to his own emotions, desires, and instincts; he is willing to stand for something by defending "his bench".
In order to avoid living in an existence of compromise, Jerry provokes Peter to kill him, as a test for himself to see that morality and ethics can still exist. Through dying, he is able to be hurt by another person, establishing an emotional connection rather than compromise.