Jerry is "disconnected." He has lost his family. He does not answer the letters he has saved in his strong box. He only loves the "little ladies" once. He has failed at the only relationship revealed in the play- the one with his landlady's dog. He does not know the woman who cries from behind her apartment door. He tells Peter the long and personal story of JERRY AND THE DOG only to hear Peter claim that he "doesn't understand." Jerry connects with Peter with a knife between them.
Although it's difficult to point to any one reason, it is clear that Jerry represents the alienated individual (a central theme in modern writing, especially existentialist writing) confronting the establishment figure in the person of Peter. Jerry is unstable; life has not been good to himas typified by the run down neighborhood that he lives in. Peter, while not rich, represents the well established middle class which would prefer to sit on the bench and read rather than deal with the misfit Jerry. Since there are many absurdist elements in the play, it's difficult to identify any particular reason why Jerry is as he is. Jerry is part of the human situation, a part that cannot find a place for itself in a world that does not seem to care, who is "killed" by its indifference.