Examine this statement as it relates to Hills Like White Elephants by Ernest Hemingway: "If Jig really loved the American man, then she would listen to him and go through with the operation."

This statement seems to be what Jig's American boyfriend thinks, but I would push back and say this is not the message Hemingway is trying to convey.
If you read the dialogue that makes up the bulk of this very spare short story, it becomes clear from the boyfriend's repetition of the same ideas, especially his lame statements that he wants whatever Jig wants, that he is insincere and doesn't really care about her or her needs. He simply wants to get out from under being on the hook for a baby.
Jig's impatient responses to him show how much he is irritating her and how tone deaf he is. He is talking at her but not communicating. She says:

"Would you please please please please please please please stop talking?"

I would argue that the tables should turn and that the real question Hemingway is asking is the opposite: if the man really loved Jig, wouldn't he at least actually listen to what she has to say and engage in a real conversation with her, instead of insistently repeating himself and trying to bully her into an abortion? If you really love a person, wouldn't you be honest about your doubts and fears? That might trigger a real conversation about a very important decision. This is not the time to be insincere and play games, but that is what the boyfriend is doing.
The question isn't whether one or the other partners is willing to sacrifice their desires out of love for the other. Instead, the question is if there is any love to salvage at all in this relationship.