Quote Originally Posted by Clistenes View Post
People were fighting on chariots before they managed to breed horses big enough to be of use as battle mounts (even more if the rider wore armor) so they got how to fight on chariots figured long before they even thought about riding horses to battle.

So the warrior classes were trained in chariot fighting before horse archery even existed... Somebody had to create it from the scratch, and the warrior class probably were like "why should we learn to do that when we can already fight on chariots?"
Plus the chariot, having a chariot, being a chariot warrior, was often a sign of prestige and status, so many of them were not going to just give that up.