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Ever wondered why we've domesticated the horses (and we've done it before we've invented writing) so the question most often arises is why we dont ride Zebras. Afterall, they are perhaps more related to their counterpart compared to chimpanzees being related to orangutans. The big problem with domestication, quite simply, is that zebras are mean. Compared to horses who bite Zebras they look behind themselves, aim and strike with purpose when they kick. The power of a zebra’s kick is enormous. It can easily shatter a lion’s jaw.
TLDR: Short answer they are so much harder and more dangerous to train. Other sources say horses follow a lead horse while zebras are more independent