- herbivores
- relatively quick to raise from birth to useful slaughtering
- high volume of usable meat from the animal (though husbandry undoubtedly guides this)
- produce useful secondary products (leather, milk, wool, eggs, garbage disposal, mechanical effort) - IMO probably the primary driver the further back you look, towards subsistence farming times
Yeh, other animals can hit some of these to some degree, but when you look at the main livestock choices it's fairly obvious to me why sheep, pigs and cows were chosen (in western Europe). If you're some family living on a farm back in the middle ages, you're only going to have capacity to raise a couple of animals and these give you the best return on your effort/resources.
Look at the central Asian Steppe region, where horses were absolute cornerstones of society for millennia due to the roaming structure of their living. Horse and horse products such as mare's milk are still products consumed there today, and it makes absolute sense that their ancestors found multiple uses for the animals their scarce resources went into keeping alive.
But I think you're missing something: seafood. We eat quite a large variety of fish, crustaceans and mollusks.
1. Friendly 2. Feedable 3. "Fecund" 4. Family-friendly