This isn’t because Greeks never had seen a person riding a horse before
Actually, this was more uncommon than you think. Horses during the ancient period were too small and weak to be ridden, at least in the area around greek and the Mediterranean sea general. Thats why everyone used chariots instead of cavalry.
Some classic origins of mythical creatures: The source for unicorns were people describing rhinos (although the horns of Narwhales were also mistaken for unicorn horns. They have such a "unicorn horn" on display in Vienna, next to the Holy Grail).
Mermaids probably come from the description of manatee.
In china there are actually snakes that jump and glide from tree to tree which could have been the source for eastern dragons.
