When the girl remarks that the hills across the Ebro valley look like white elephants, the man responds that he has never seen a white elephant, to which she replies, "No, you wouldn't have." This irritates him, suggesting a deeper significance to the comment.
White elephants are very rare and were once given to nobles at the court of Siam as a mark of the king's favor. The upkeep of these animals, however, was so ruinously expensive that they eventually came to symbolize the exact opposite, and the king would give them to those he wished to harm. The current meaning of the term "white elephant," therefore, is something expensive and useless.
There remains the question of why the white elephants were so expensive to keep. They were smaller than ordinary elephants, meaning that they would theoretically cost less to feed. However, they had to be given special food and washed in a particular way because they were sacred. The idea of a white elephant in the story, therefore, is a complex symbol. To the man, it means something expensive and useless, which would limit his ability to do as he likes. To the girl, it means something sacred, which it would be an abomination to kill. In each case, the white elephant stands for the girl's unborn child. It is, however, an indictment of soulless modern society that it takes the side of the man in giving the term "white elephant" its commonly understood meaning, instead of perceiving it as something sacred.