How did Freud and Lévi-Strauss read the same Oedipus myth so differently?

They disagree about what a myth is for. Sigmund Freud read the Oedipus myth as a window onto the mind of every child. Claude Lévi-Strauss read it as a logical machine. Both thought the myth was universal, and both theories have been criticised as hard to test.

Freud first. In classical psychoanalytic theory, the Oedipus complex is a son's sexual desire for his mother and hostility toward his father, first formed during the phallic stage of psychosexual development. In The Interpretation of Dreams (1899), Freud proposed that an Oedipal desire is a universal psychological phenomenon innate to human beings and the cause of much unconscious guilt. He explained the play's power this way: the destiny of Oedipus moves us only because it might have been ours.

Lévi-Strauss asked a different question. If the content of myth is arbitrary, how can myths throughout the world be so similar? His answer was structure. He believed there was no one authentic version of a myth, so he looked for the fundamental units of myth, "mythemes". In the Oedipus story, he found oppositions: the overrating and the underrating of blood relations, and the autochthonous origin of humans and the denial of it. For him, the job of myth was a sleight of hand, associating an irreconcilable opposition with a reconcilable one, creating the illusion that the former had been resolved.

Both have drawn the same criticism. Freud's theory yields few testable predictions, according to Daly and Wilson. And structuralism's main propositions were not formulated so that they could be subject to verification or falsification.