He refuses to yield Catherine to 'duty'—he will force an interview, consent or refusal be damned.

“That is quite possible,” remarked Heathcliff, forcing himself to seem calm: “quite possible that your master should have nothing but common humanity and a sense of duty to fall back upon. But do you imagine that I shall leave Catherine to his duty and humanity? and can you compare my feelings respecting Catherine to his? Before you leave this house, I must exact a promise from you that you’ll get me an interview with her: consent, or refuse, I will see her! What do you say?”