The Sphinx is the daughter of the mighty monster Typhon and the immortal serpent-nymph Echidna.  Hesiod said  the two-head dog Orthros, son of the above pair,  sired the Sphinx on his sister the lion-fronted Chimera.  Artists portray the Sphinx with  the head, breasts and arms of a goddess, the body of a lioness and the wings of an eagle.  Sometimes she wears a snake for a coronet or has a serpent tail.  Some surveys say her name is Phix.    Hera probably had a hand in raising the Sphinx after all she nursed two of the Sphinx’s siblings the multi-headed Hydra and the Nemean Lion.  Hera, the Queen of Olympus, who summoned the Sphinx from the most distant part of Aethiopia when the gods cursed the ancient Greek city of Thebes.  Her name means “strangler”. 

Pausanias reported that from a rocky knoll named Mt. Phix in her honor, the Sphinx, chanting a riddle, sallied forth to bring death upon those she caught.  This ancient riddle was taught to her by the musical Muses on Mt Olympus. Passerby who failed to answer the riddle properly were eaten.   Creon, the perpetual regent of Thebes,  offered the hand of Queen Jocasta and the kingdom of Thebes to whomever would rid them of this deadly, man-seizing plague.  Some authors say that once the riddle was answered the “flying” monster would throw herself form the cliffs and die on the rocks below.  It seems more likely that Hera had a place of honor for her in Olympus where her voice could be joined with the chorus of the muses.  

The prodigal prince of Thebes, Oedipus came along to claim the crown.  According to Robert Graves, prior to the Dorian invasion led by the children of Heracles, the Ancient Greeks sacrificed their kings when their power waned.  Oedipus was to be the next sacrificial king.  He too would be replaced in twenty years or so when a plaque fell upon the city again.  But, if the kings come and go, the queens must provide the stability to society. They were a matrilineal society.  The crown passed from mother to daughter.  As Ugi Brodi points out,[i] if Jocasta is queen of the city,  the flip side of that coin is the Sphinx on the hill outside. Two faces of the same coin; sister serpent-nymphs. The Sphinx’s mother was a dragon and Jocasta’s father was sown from dragon’s teeth.  Bill Blomfield, points at this theme of monstorisity and incest that enters into the story with the Sphinx and continues in the life of Jocasta.ii

The Sphinx was called a “singer”. Sophocles wrote of her; a “chanting fury” .  The chanting of the Sirens brought death passing sailors.  The Sphinx’s riddle brought death to passersby, until it was Oedipus who passed by.  The question she asked was, “What is it that walks on four legs I the morning, two legs during the day and three legs in the evenings?” It’s ironic that Jean-Auguste-Dominique Ingres’ painting, probably the most famous modern rendering of this scene shows Oedipus leaning on the two spears carried proverbially by Achaean warriors.  Oedipus’ very name means lame-foot; a lameness he’d known always.  

Oedipus answered “Man.” Not an obvious answer in his case. Probably better than “Oedipus”

 What about the answer;  “Woman”?  Robert Graves divided the lives of women into similar three parts and must sharper sub-divisions than can be seen in the life of a man.   If the riddle hints at the ages of a woman, then the Sphinx's question reflected  a vision of the triple essence of all reality.  The moon, waxes, wanes or is full.  The Sphinx herself being of a dive nature had a trips shape; woman, bird and lioness.  Woman are “maid, mother and crone” by Graves theories. The answer “Woman” in reference to the Sphinx doesn’t work too well, her being a divine monster walking on four feet. That just leaves Jocasta as the reference to “Woman”.  

But if by saying “man” Oedipus meant to claim the crown in his father’s name rather than his mother it would indicate the end of Sphinx/Jocata’s matrilineal reign . Jocasta becomes just another princess whose husband or father is slain; she and her kingdom become the property of the invader like Clytemnestra and Agamemnon.   The Sphinx would be just another monster that must be slain before the hero can marry the princess and claim the kingdom, like Bellerophon slaying the Chimera and wedding Philonoe.    The only difference here, is that the monster sings.