How we cite our quotes:
It would degrade me to marry Heathcliff now; so he shall never know how I love him: and that, not because he's handsome, Nelly, but because he's more myself than I am. Whatever our souls are made of, his and mine are the same; and Linton's is as different as a moonbeam from lightning, or frost from fire. (9.92)
Though she loves him as her own being, Catherine sees Heathcliff as beneath her compared to the social promise of marriage to Edgar. It's hard to reconcile such profound love with the choice she makes, but somehow she manages to work out the logic in her head.
My love for Linton is like the foliage in the woods: time will change it, I'm well aware, as winter changes the trees. My love for Heathcliff resembles the eternal rocks beneath: a source of little visible delight, but necessary. Nelly, I am Heathcliff! He's always, always in my mind: not as a pleasure, any more than I am always a pleasure to myself, but as my own being. So don't talk of our separation again: it is impracticable. (9.101)
To Catherine, she and Heathcliff are one and the same; thus marriage to Edgar does not mean leaving the man she really loves. That Heathcliff sees her marriage as a betrayal is what ultimately divides them.
His new source of trouble sprang from the not anticipated misfortune of Isabella Linton evincing a sudden and irresistible attraction towards the tolerated guest. (10.82)
Isabella's love for Heathcliff is one of Edgar's biggest nightmares. As children, he and Isabella had mocked Heathcliff together. Edgar still treats the adopted Heathcliff as one of the servant class.