For an animal to be domesticated and bred, it must be willing to breed in man’s company. Livestock are chosen based on many different characteristics. The lack of any single characteristic dooms effort at domestication and production.
Once the animals were found to be suitable, farmers allowed the livestock to roam freely and breed. However, they have also been instances where farmers chose selective breeding, which is the process of selecting an animal for its genetic trait and breeding the best to the best. This would result in purebred livestock with a superior bloodline and stable genetic traits.
Why were so few animals domesticated?
Because of the fact that animal domestication requires all 6 criteria which are:
A diet that can be supplied easily and relatively cheaply by humans
A relatively fast growth rate with short time intervals between births
The ability to mate and breed in captivity
A tendency toward calm, predictable behavior rather than panic
A lack of viciousness toward humans
A social structure based on hierarchy and cooperative group living without strong territorialism
Humans tried to domesticate many other types of animals that could be useful for work or provide a good meat source, but these attempts have been unsuccessful.
One of the most notable examples is the Zebra as they have a tendency to panic easily, are notoriously bad-tempered around humans and have never lost their tendency to bite unexpectedly. Hence, ancient herdsmen have failed for centuries to domesticate zebras. Although they are genetically very similar to horses and can even breed with horses, their behavior is quite different.