The most famous Centaur story, the centauromachy, describes the Battle of the Lapiths and the Centaurs, which is often taken to symbolise an inner conflict between “civilised” (Lapith) and “wild” (Centaur) urges, but really is more subtle than that.
The Lapiths were cousins of the Centaurs, as both were descended from Ixion. The Lapiths were human, and were a race of master horsemen from Thessaly credited with inventing the bit mouthpiece. The Centaurs were half human, half horse. Both of them are heavily involved with horses (the wild side) in different ways, and in this time and place with no cars, the ultimate in speed, power and penis-extension would be a horse.
The most obvious difference between the two is that the Lapiths can get off their horses. You could say that they project the wild side of their nature outside themselves and then attempt to control and manipulate it, whereas the Centaurs’ only option is integration. Integration is a rarer and more difficult solution, but it’s the holistic approach that represents true mastery (e.g., Chiron). Centaurs who can’t do that yet, continue to struggle within themselves and this manifests externally as a tendency to fight.
The Centaurs started the battle with the Lapiths by getting drunk and raping the bride. This seems like a clear picture in myth of the human fear of what might happen if the controlling mind (in this case dulled by alcohol) doesn’t keep the instincts (the horse end) reined in at all times.
But Centaurs who are truly in touch with their instincts don’t behave like that; a wild horse’s natural instinct is always to flee from trouble, not to start a fight. This is an example of our fear of this side of our nature, which doesn’t match the reality. The Centaurs’ aggression is caused by the confusion in their human heads, not by the horse end of the equation. A horse symbolises wild and free, not drunken violence, which is more of a human trait. You could say a Centaur’s what you get when you cross a horse with a dangerous animal.
If you attach the average human mind to all that horsepower, you get huge potential for great things and also for errors. The integration process takes time. The Lapiths’ combination of denial and control is more outwardly successful in the shorter term, which is why they’re usually considered to be the civilised ones, but really we know this method doesn’t exactly work either (it certainly didn’t for Ixion). They both have their problems.
The centaur planet Crantor is named after a well-liked young Lapith accidentally killed in the battle, and Ixion is a TNO. Elatus, another centaur planet, was a Centaur, but there was also a Lapith of the same name.