What is the irony in "Hills Like White Elephants"?

With  being a
contrast between what a character thinks and what the reader or audience know to be true, the
reader must seek the difference between what the characters think and what he/she discerns about
them.

Since the girl mentions the hills being like white elephants, she
understands their meaning:  She tells the man who says he has never seen a white elephant,
"No, you wouldn't have." She is the one who expresses doubt about having an
abortion.  But the young man, who tries to convince the girl to have the operation, says that
everything will be all right and the couple can return to their life beforehand. (He
"buys" the white elephant, something one thinks has value, but does
not.)

The irony of the title, then, is that the man "buys" a white
elephant believing that the action under consideration can return him and his girlfriend to
their former relationship, but the girl, like the reader, knows they will never be the same, for
she turns from the vision of life, fields of grain and trees, and agrees to the man's putting
their bags on the "other side of the station."