The special thing about a horse isn't its body, it's its mind. They are relatively easy to domesticate and will accept, basically, that an alien bipedal creature sitting on its back is a part of the herd and that it's okay to listen to and obey this thing. Nobody has ever ridden a zebra into battle because they are stubborn, untrainable, love to bite and not let go and are comparatively rambunctious in their herds and therefore hard to keep. The degree to which we domesticate animals is almost always in proportion to how easy they are to domesticate and this usually comes down to behavior more than anything. We eat chicken eggs instead of ant eggs because chickens don't attack us and are easy to keep in enclosures unlike ants. We ride horses (and a select few other animals) because they are fairly docile, easy to command, and don't often challenge the systems or structures we use to control them when they're off duty.

Cows aren't as fast or agile and most antelopes don't lend themselves to domestication (although there have been some attempts, with the eland for example).

Horses are simply better. The natural world of a horse is a herd dominated by a single male. When humans domesticate horses, they are effectively replacing that one stallion in the horse's mind. Very few animals operate like this and lend themselves to domestication, and of those who are, the horse just happens to be strong enough to carry an adult human on its back (something dogs and smaller ungulates like llamas, sheep or goats can't do) and the fastest and most agile of those who can do (large bovids, camels and asses).