It is interesting that Hemingway does not mention the name of the man and that he also refers to Jig mostly as merely the "girl." While there is an impersonalization to both characters, nevertheless, the American's sang-froid in discussing the disposal of what is his baby as well as hers certainly affects the reader's perception of him. Added to this, of course, is the natural tendency of the reader--especially female readers--to sympathize with the girl who must bear the burden of pregnancy and, if she aborts, all of the emotional trauma to her body as well as much of the psychological and spiritual ramifications.
As the previous post has so cogently remarked, the reader's involvement with the narrative makes it difficult to objectively determine the direction of the conversation. But, it does seem substantiated that the girl bears the burden of their pregnant act (excuse the pun). For, she, better than the American, foresees the consequences of the "perfectly simple" operation: "Then what will we do afterward?" Also, in her desire to keep the man that she loves, she tries to agree with him:
"And if I do it you'll be happy and things will be like they were and you'll love me?..But if I do it, then it will be nice again if I say things are like white elephants, and you'll like it?"
But, the girl's practical sense overcomes her emotional wish, and she realizes that if she has the abortion, things will not be the same:
"No, it isn't. And once they take it away, you never get it back."
In his minimalist method, Hemingway does not mention what the "it" is. However, the reader understands that the girl means that they can never return to their more innocent state.