From what I hear, most zebras do not make great "pets"
They are similar to a mule/donkey training style, very stubborn and can be real Jack-A$$es. (No pun intended. )
I have a friend that has a Zebra stud and a yearling filly now. (Not related) and she is crossing the stud to Mini-Donkeys, Donkeys, Ponies and Horses. Ze-Donks are so freaking cute. The filly she had earlier this year had SUCH dun factor, you wouldn't believe it. She is beautiful.
Full photo credit to: Rarity Acres. ^^^ She's for sale. Wouldn't that be something to play with all day long?
Take a look at this website. It gives some pretty good information about Zebras as pets. I was looking into one a while ago is why. Basically, they train and react like a donkey. They have virtually no withers, and are generally under 13hh.