The tradition holds two incompatible centaurs at once. The Thessalian tribe is a byword for what happens when appetite has no restraint: invited to a wedding, they get drunk and attempt to carry off the bride, and the resulting battle is the centauromachy. Against them stands Chiron, who is temperate, learned in medicine and music, and tutor to Achilles, Jason and Asclepius. The sources explain the difference by giving Chiron a separate parentage, which is an admission that the type does not otherwise permit him.
The centauromachy was carved on the south metopes of the Parthenon and on the temple of Zeus at Olympia, and in both places it does political work. Greeks against centaurs reads as order against disorder, and after the Persian wars it reads as Greek against barbarian. That is a use of myth for argument rather than for storytelling, and it is one of the clearest surviving cases of it.
A theory that will not go away holds that centaurs record the first sight of mounted riders by people who did not ride. It is attractive, it is unfalsifiable on present evidence, and the Greeks who told the stories were themselves horsemen. It belongs in the entry as a proposal that has been made repeatedly rather than as an explanation the sources support.