The Joker tells conflicting stories about his scars because he has no interest in a conventional origin story; his true origin is his complete lack of one. When he tells the mobster Gambol that his abusive father carved his face, he appeals to a classic psychological cliché of childhood trauma. When he tells Rachel Dawes that he mutilated himself to comfort his disfigured wife, he plays on romantic tragedy. In both instances, he tailors the narrative to exploit the specific emotional vulnerabilities of his victims. If he had finished his story to Batman during the climax, he likely would have invented a third variation. By constantly rewriting his past, the Joker rejects the basic narrative rules of character motivation. He understands that society craves a rational explanation, a neat psychological trauma to explain his evil. By denying them this, he remains an elemental force of nature rather than a broken man who can be understood or cured. He has no past, no real name, and no fingerprints. The truth behind his scars is irrelevant; the scars are simply a physical manifestation of his philosophy that life is a cruel, chaotic joke without a punchline.