Statue of Chiron, the wisest of all the centaurs and the teacher mentor of the ancient Greek hero Achilles (Sculptor: Anna Hyatt Huntington, 1936)

Centaurs according to the Greek mythology were monstrous creatures. With a human head, arms and upper body and the body and legs of a horse. Centaurs, male and female, lived on mountains and in forests. They fed on raw flesh, could not drink wine without getting drunk. Centaurs went about in herds and were very prone, if male, to rape mortal women.
They represent man’s animal nature. At the same time as any other creature having a human head and an animal body the union of the ‘spiritual’ and the ‘material’ world, the, conscious and the unconscious human behavior. As half man, half horse we have conflict of primal nature (wild behavior) versus civilized nature (educated, refined behavior in Chiron).
The most realistic view on Centaurs is that they were a Greek tribe in Thessaly during the Bronze age. They were excellent horsemen, that ‘s why they became a legend, as a half man-half horse creature.
It is not a coincidence that the ancient Greeks, placed on the south side of Metopes of the Parthenon the temple of Goddess Athena (the goddess of wisdom and arts), imprinted the Centauromachy. They simply wanted to signify the struggle between the forces of civilization, philosophy, science order and justice, on the one hand, and irrational chaos and barbarism on the other.