The main claim of the text seems to revolve around communication or the lack of it. The American and the girl, Jig, are really bad at communicating effectively with one another. The fact that neither of them ever actually mentions, explicitly, what it is that they are discussing—a potential abortion for her—is so indicative of their relationship. The American seems clearly, to the reader, to want the young woman to get the abortion, as he keeps describing how "easy" and how "simple" a procedure it is. However, Jig seems to be more concerned about their romantic relationship and its future, how the "procedure" might change things or if it will help them return to the prior contentment they seemed to feel before the unwanted pregnancy, the so-called "white elephant."
The fact that neither person is called by their real name in the story also contributes to our sense that we don't really know them, and they don't really know each other either: the man is only ever called the American, and he refers to her as "Jig," an apparent nickname. By the end of the story, she has become upset and has asked him to stop talking multiple times. In the end, she says, "I feel fine [...]. There's nothing wrong with me. I feel fine," when she obviously is not fine at all. She seems to have given up even attempting to communicate honestly. It becomes clear that a successful relationship and the happiness of its members depends on good communication.