This story has often been discussed in eNotes. I think most readers have agreed that the man and woman are going to Madrid for her to get an abortion. They have evidently been discussing the matter for a long time before the opening of the story. She must have been pregnant for at least a couple of months, so they would have had plenty of time to talk about all aspects of their problem. There is no need to name it now that they are already on their way to Madrid. Besides that, what they are doing is illegal, so they have to be rather guarded in their conversation. The different attitudes of the man and woman are obvious throughout the story. He wants her to have the abortion and she wants to have the baby. He feels that a baby will tie him down, and evidently they have been leading a gypsy sort of life (characteristic of Hemingway in the 1920s; he wrote about this Lost Generation wanderlust in his novel The Sun Also Rises), traveling all over Europe, where everything was cheap and, unlike in Prohibition America, liquor was legal, and abundant. At one point Jig says, "That's all we do, isn't it--look at things and try new drinks?" She wants to have the baby because women who are pregnant generally want to have their babies. This hardly needs explaining. The reader feels sorry for the girl and feels contemptuous of the man who is forcing her to go through with something she hates even to think about, much less talk about.
Here are two exchanges of dialogue which should explain practically everything:
She says: "Doesn't it mean anything to you? We could get along."
He says: "Of course it does. But I don't want anybody but you. I don't want any one else."
He doesn't want a third party. He doesn't want the baby. What else could he be talking about?
You can find all kinds of information about this story in eNotes using the links below and others. It has probably been more thoroughly discussed by eNotes members than any other Hemingway short story.