Well, not exactly.
A zebra is to a horse what a wolf is to a dog.
Is a wolf a dog?
Well, yes, in a way.
But no, you can't really domesticate them.
Yes, there are people who keep wolves as pets. It's a really bad idea. The wolf, if it grows up as a puppy, can beocme very attached to the household, but it's not a dog. It's a wolf, and it's never very comfortable around other people. It looks like a dog, maybe a husky, but it doesn't ACT like a dog. It's not friendly. It's extremely protective of the family, and it's a dangerous beast inside the house. No, not (necessarily) dangerous to the family it loves and is part of, but dangerous to everybody else, including invited guests.
Wolf puppies are like bear cubs: they are playful and friendly, but grow up to be wolves and bears. Maybe they like YOU, but they do not like our SPECIES; dogs do. Zebras are probably like that.
"Well, not exactly.
A zebra is to a horse what a wolf is to a dog. "
Dogs are derived from wolves that were domesticated thousands of years ago. The horse and zebra were probably the same species a hundred thousand years ago. Zebras today are probably much like Horses were when they were first domesticated. Over time with selective breeding, desirable traits are enhanced and the species diverge. I bet ancient Europeons would have no more trouble domesticating the Zebra than the original horse.