They are unpredictable and are known to attack people. To be domesticated, animals must meet certain criteria. For example, they must have a good disposition and should not panic under pressure. Zebras’ unpredictable nature and tendency to attack preclude them from being good candidates for domestication.
While attempts at domestication have failed, some individuals have had success training and even hybridizing zebras! Common zebra hybrids: Zorse (horse + zebra) and Zonkey (donkey + zebra). Zebra hybridization has actually been in existence at least a century. One of the pioneers in the field was J.C. Ewart, author of The Penycuik Experiments in 1899.