I've received an email stating that, "gee means right, haw means left."
In the United States and Canada, that does hold true.
However, in England and other countries in the United Kingdom, and in Europe, Gee and Haw are reversed. Gee signals the animal to turn away from the driver's side and Haw signals the animal to turn toward the driver's side and, as people from North American who visit England, Ireland, Australia, New Zealand, and Europe discover, the cars and trucks have the driver's wheel in the passenger's seat and you drive on the wrong side of the road.
That conforms to the same driving convention from the times of horse drawn vehicles. With the driver on the other side Gee and Haw get turned around. The Centaurs learned from their Maori Mentors. They came from New Zealand and so their Gee and Haw are reversed. That is also why Pegasia moved to the right side of the Centaur Way when Kix was confused by her first call of Gee. Once she was in position Kix was accustom to, Gee told Kix to turn left.