The contradictory element in the story is that there is a subtext of emotional dynamics transpiring between the man and the woman. The contradictory element is that neither of them are speaking openly to one another about what they want. For example, the man wants the woman to have the "procedure" which is an abortion. Yet, rather than tell her outright that he wishes her to have an abortion, he contradicts his own intent by saying that it is "her choice." With all his references to the ease of the procedure, it is contradictory that he insist in this when his own personal sentiments are that he will most probably leave her if she does not have the procedure. The woman is much the same way. She feels different expressions about the condition in which both of them are in through her subjective. Yet, her outward statements seek to articulate simplicity and a sense of lucidity, when her emotional state internally is far from this point. For example, when she talks about how they can be happy towards the end of the story, this is a complete contradiction than the emotional state she is experiencing. In this, there is a clear and definite contradiction between what is felt and what is spoken. It is Hemingway's genius that he is able to bring out the difference between what is felt and what is said in a relationship.
In this story, a man, the American, has a conversation with his girlfriend Jig, who is pregnant. He wants her to have an abortion. She does not, seeing the possibility inherent having a baby. The contradiction is that he thinks it is freeing to get out of having the child, but she realizes that they can't have everything. Every choice is in fact a choice. In the dialogue below, she points out the contradiction in his "have-it-all" thinking. Hemingway's writing is notably spare, and he leaves it to the reader to supply the he-said/she-said information, so I have taken the liberty, for the sake of clarity, to supply the he said/she said below. When she says "we could have everything," one interpretation is that she is mocking him, because she then turns around and contradicts her (really his) words, saying that, in fact, no they can't:
"And we could have all this," she said. "And we could have everything and every day we make it more impossible."
"What did you say?" [he said]
"I said we could have everything." [she said]
"We can have everything." [he said]
"No, we can't." [she said]
"We can have the whole world." [he said]
"No, we can't." [she said]
"We can go everywhere." [he said]
"No, we can't. It isn't ours any more." [she said]
"It's ours." [he said]
"No, it isn't. And once they take it away, you never get it back." [she said]
She is wiser than he is and understands that an abortion will be a choice they can't take back. They can't have everything: one choice precludes another. They can't have an abortion and pretend everything is the way it was before. His notion of freedom and having the whole world is limited and immature.