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Half man - half horse. Not as much of a stretch as half woman - half fish, you know? Chiron was immortal because his father was Saturn, who shapeshifted into a stallion just as his wife checked to see if he was fooling around on her. His mother was the Oceanid Philyra, who was so freaked out by the child she had delivered that she begged the gods to change her into anything NOT anthropomorphic, so she was transformed into a linden tree.
Chiron was an exception among centaurs because of his level of mind. He was considered the most wise and most just being of all, human or animal, and was therefore entrusted with the care of many heroes and children of the gods. He is often shown with human front feet in the oldest images, but more recent images were created to make him more of an animal nature, sometimes even giving him floppy ears. He is shown clothed to indicate his civilized nature.