The reason we can claim this story conversation, or dialogue, is about an abortion is because the American man gives a clue to the topic substance. He says, "It's just to let the air in."
"It's really an awfully simple operation, Jig," the man said. "It's not really an operation at all."
The girl looked at the ground the table legs rested on.
"I know you wouldn't mind it, Jig. It's really not anything. It's just to let the air in."
The girl did not say anything.
"I'll go with you and I'll stay with you all the time. They just let the air in and then it's all perfectly natural."
One of the types of procedures for abortions is called aspiration. The American man might simplistically understand it as letting "the air in." Of course, his understanding is simplistic and limited as is illustrated by his correlated remark that it's "not really an operation at all" and that Jig "wouldn't mind it." So it is very probable that the man understands the whole procedure in simplistic terms as letting "the air in."
Another clue is that later on in the story he says, "I don't want anybody but you. I don't want any one else. And I know it's perfectly simple." This allows us to infer that (1) if Jig does not do "it,"which is perfectly simple, they will no longer be alone; they will be more than "anybody but you"and the American man, and (2) that which will intrude upon just the two of them can be eliminated with the "perfectly simple" procedure that is "not really an operation at all."
These clues combine to paint the picture of an unplanned pregnancy and an upcoming--though still being debated and discussed--procedure to rid them of it. Though not an entirely true description, Hemingway reveals enough through the man's limited thoughts for us to piece the ideas together with a little detective work to arrive at an abortion as being the topic.
Abortion is a very sensitive topic to discuss, but the man made it appear as if it's something that could be done with just one breath of the air. And the very gullible jig seemed to take in every word he said. It is very apparent the decision on what should be done with their "little problem" was controlled by the man alone.
When the girl tried to tell the man about her hesitations with regards to underoing the "small operation", the man made it appear as if it's her decision to make, but it is evident with his words that he really doesn't want the baby! (What do you think would that make her feel?)
Abortion is a decision where both man and woman concerned should be involved. The woman should not indulge in the muder if she doesn't like to. Women should not be persuaded, for we women have our own thinking and feeling minds. We should know how to stand up for what we believe in.
The focal argument is over a "simple" operation. The American wants the girl to have it, but she does not. Since she is just a "jig" a short dance or relationship, he does not want to be tied down. The young girl wants more (she disparingly comments all they do is look at things and try new drinks). When she looks out at the hills (representing a pregnant belly), she looks out longingly. The American is not interested though.
The dialogue about having everything and never getting it back is also representative of how each sees the situation he/she is in. Notice the "it" isn't ours anymore. The "it" is the baby they are planning on aborting.