Lady Betty has no interest in the Duke of Collingham. She doesn't care that he's fabulously wealthy, or devastatingly handsome, or impeccably well-dressed. All she sees is an arrogant nobleman with an abrasive personality and an annoyingly persistent streak.
And the Duke of Collingham is persistent. He can have any woman in the whole of Society--but the one who won't have him is the only one he wants. And he'll stop at nothing to persuade her.