
"The Rocking-Horse Winner" is a short story by D. H. Lawrence. What is ironic about the title?
To my mind, at least, the central irony that creates the conflict that runs through the whole story is introduced to us in the first paragraph when we meet Paul's mother. Note how the text presents her:
She had bonny children, yet she felt they had been thrust upon her, and she could not love them... Everybody else said of her: "She is such a good mother. She adores her children." Only she herself, and her children themselves, knew it was not so. They read it in each other's eyes.
The irony of this passage is that the mother appears to love her children, and gives every visible proof of her affections through her actions, but this cannot prevent the reality of her heart "turning hard" whenever she is with them. It is this lack of love that drives Paul to go to such supernatural lengths to gain money to make his mother happy, and therefore gain her genuine affection. Note how this irony is referred to again at the end of the story by Uncle Oscar, her brother:
"My God, Hester, you're eight-odd thousand to the good, and a poor devil of a son to the bad. But, poor devil, poor devil, he's best gone out of a life where he rides his rocking horse to find a winner."

