It closes the possibility that somebody might think the horse rides the human.
In the old days, when people commonly rode horses, some might have preferred to ride in the vehicle being pulled by the horse than directly on its back I'd suppose . . .
I see usage nowadays is more in the US and popular, so probably it's more in contrast to trick/stunt riding, as in western movie shootouts.
The rest is just historical surmise, when language was not standardized and people got around this way. Variations of 'horseback riding' go back to the 1300's.