Because they evolved in a place where literally everything else wants to eat them, zebras are extremely hard to tame.
A horse might freak out and buck its rider off, but a zerba will freak out, buck its rider off, kick the shit out of the rider until they stop moving, and then run away never to be seen again. So historically there are few instances of people taming zebra let alone getting them to the level of loyalty needed to be used in calvary.
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