When Linton insults him when they are still children, Heathcliff tells Nelly clearly about his plans for revenge: "I am trying to be settle how I shall pay Hindley back. I don't care how long I wait if I can only do it at last" - "I only wish I new the best way. Let me alone and I'll plan it out, while I'm thinking of that, I don't feel pain." His going away and becoming a “gentleman” are part of his plan to get back at Linton for taking Cathy away from him and for insulting him. Insulted repeatedly by everyone as a child, as a matter of fact, except for Cathy, Heathcliff seeks revenge against life in general. When he returns, he is described in Satanic terms. For example, Isabel says he has"sharp cannibal, teeth, basilisk eyes." His revenge is a form of rebellion in that he wants to overthrow the class system and prejudice that turned him into “a dirty, filthy child” (in Linton’s view) and resulted in Cathy preferring to marry a man with money, and in doing so betray their love.
Heathcliff was fixated on Catherine, and felt he had a right to her love. Her rejection of him caused him to lose most of his human qualities. He torments those around him, has disdain for his son, his wife, and eventually his vengeful force kills Catherine.
Even in death, he does not appear to be at peace, as if he is taking his anger and need for revenge with him.