In The Zoo Story, what is the meaning of Jerry and the dog?
"The Story of Jerry and the Dog" is about Jerry's desperate attempt to connect with his landlady's dog, which tries to attack him every time he enters his building. The story is about the lengths to which Jerry will go to form some relationship with the dog, either as friend or enemy. He goes from feeding the dog to trying to poison it, but in either case, but the dog remains indifferent. The suggestion is that the world is immutable and unknowable, at least to Jerry, who tries so hard to leave a mark, but who always, in the end, is alone. The best he can do with the dog is achieve an uneasy truce: the dog simply ignores Jerry. As Jerry says at the end of his speech: "I have learned that neither kindness nor cruelty by themselves, independent of each other, creates any effect beyond themselves; and I have learned that the two combined, together, at the same time, are the teaching emotion. And what is gained is loss."
In another sense, "The Story of Jerry and the Dog" is simply a recapitulation of the larger story of Jerry and Peter. Jerry is trying to make some impression on Peter, like he did with the dog; the games Jerry played with the dog are similar to the ones he plays with Peter in trying to draw him out. In this case, the meaning of the story with the dog becomes larger than a simple anecdote -- it becomes a kind of parable for modern life.
Desperate to communicate with Peter or at least to teach him something about the difficulties of communication, Jerry comes up with "The Story of Jerry and the Dog." It is a long, disgusting, and eventually pathetic tale of his attempt to find some kind of communication, or at least relationship, with the vile landlady's vile dog (the hound who guards the entrance to Jerry's particular hell). Jerry fails to reach the dog, though he goes from trying to kill it with kindness to just plain trying to kill it; the two finally achieve mutual indifference, and Jerry gains free entry to the building without being attacked.
Jerry's story about his landlady's dog could be seen as an allegory for his own inability to relate to others. In the end, Jerry says that he and the dog harbor "sadness, suspicion and indifference" for each other, which is similar to the relationships that Jerry has with other people.