In this story, the American and the girl, Jig, are a couple in love who travel around, seemingly carefree. And although this story consists mostly of dialogue and small talk, the couple are actually having a debate on whether or not Jig should have an abortion. The man clearly wants her to have the abortion because he does not want anything to interrupt their carefree, traveling (yet somewhat empty) lifestyle. I mention empty because as Jig notes, "That's all we do isn't it--look at things and try new drinks?"
A white elephant is something rare in nature. In certain religions (Buddhism) and cultures, it is sacred. The image of the hill (womb) looking like a white elephant is Jig's way of saying this is something new and perhaps promising even if it interrupts the lifestyle they've become accustomed to. The man looks at the potential child as a burden. This is the main conflict. While he presumes to be supportive of her decision, he is definitely pushing for her to have the abortion. She, on the other hand, agonizes over the decision in order to make the best choice. The man wants to continue their way of living. Symbolically, he wants to continue looking at hills as hills. But with this pregnancy, the woman begins to see things differently. She dares to wonder about a different kind of life. So, she starts seeing things differently. The hill looks like a white elephant. It is something unexpected and perhaps something she (and he) should think about with more consideration.