In "Hills Like White Elephants", how would you describe the relationship between the man and the woman?
You asked more than one question so I have had to edit your initial question and form it into a more general question about the relationship between Jig and the man in this excellent short story.
When I think of the relationship between them I think of the power that the man has over Jig and how he is forcing her to get an abortion. What we are shown in this short story is that Jig constantly changes her perception to fit with her partners, and not just with the abortion, that as we finish the tale, we know with a sinking heart that she will get, but in other ways to. Jig towards the beginning of the story makes the unlikely comparison between the hills and white elephants, yet later on, after a little fight over whether or not the man has seen a white elephant, she changes her opinion and says:
"They don't really look like white elephants. I just meant the colouring of their skin through the trees."
This is a relationship where the woman is forced to be moulded into what the man wants her to be. Jig realises the truth of the relationship and what it is doing to her, and of course, what it will do to her unborn child, in her repeated insistence that, once the operation is performed, they can't have "everything":
"We can have everything."
"No, we can't."
"We can have the whole world."
"No, we can't."
"We can go everywhere."
"No, we can't. It isn't ours any more."
"No, it isn't. And once they take it away, you never get it back."
Note here how the man is repeatedly trying to persuade Jig that everything will be alright after the abortion, but Jig knows better, and she knows how irrevocably it will change things, yet she clearly lacks the strength to make her will felt and her voice heard. At the end of the tale she has suppressed herself and moulded herself once more to his wishes, burying her true self just as surely as she will bear the unborn child she is carrying.