Why are you supposed to care? Well, hmm. I don't know. What I like are the amazing weird moments -- in Mulholland drive, the woman singing/lip-syncing who collapses; in Lost Highway, the scene where the mystery man is in two places at once and has Bill Pullman call him; the tailgating scene in Lost Highway. Are the movies pretentious, self-indulgent, sometimes incoherent, and intentionally impenetrable? Yes. Some people like that. I don't. But I think there are particular scenes that are really exciting.
I think part of the "Lynchness" of Lynch movies is he clearly doesn't care whether you care. Or he wouldn't pull some of cinematically masturbatory crap he throws into a lot of his work.
I’ve been trying to follow Twin Peaks for the first time this winter. It just seems like a kooky soap opera. I get a kick out of the really cheesy music and melodrama. But I really don’t care about any of the characters and that’s pretty deep flaw in any story. I general appreciate a weird or dark sense of humor, but I see no humor at all in this.