The Zoo Story is a mixture of both realistic and absurd elements. Albee maintains that he met many prototypes for Peter and Jerry while working for Western Union delivering telegrams to rooming houses. Yet, as the play progresses, the prevailing tone steers decisively towards the absurd and the dialogues between the two characters take an increasingly inconsequential direction. Thus, in a play of this type, we shouldn't try to find rational and logic explanations for the characters' behavior. The underlying message of the play is to comment on the absurdity of human existence. In this absurd context, death becomes a way for Jerry to triumph over Peter as he successfully leads him to do what he wants.
I just saw "Peter and Jerry," last night (having seen the original "Zoo Story" when it was first produced in New York City) many years ago.
IMO . . . by rushing into the knife held by Peter, Jerry achieved the almost-orgiastic level of intimacy he craved. He connected, finally, although in the most bizarre, savage way. Taking pills or hanging would have been like a tree falling in the forest.