Everything from bacteria up to your cousin or a flying vampire unicorn can be domesticated.
Given enough weapons, you'll always find a way to enslave things for your pleasure.
Although farming animals is 100% not efficient cause, for example the soy and grains a cow eats in a day would be just enough to feed 25 more people than you would feed by farming and killing a cow in a day, usually cows are eaten when they reach the age of 10 or 15 so multiply 10 years per 365 days then multiply it by 25 and the results are; by non-farming a cow you could feed 91 more people for the lifespan of said cow.
If you want, multiply it by a single small farm of only 113 cows and the numbers start to become absurd. that's why 70% of world's cultivations of edible grains are used to feed animals.
Sure logically you may say grass fed animals instead of grain fed ones would solve the problem, But this way there would not be enough land on earth to feed all the cows, even after cutting down every single forest.
In the end animal farming takes way more that it gives, it's only an additional cost to a population not a benefit.
Then why does farming even exist if the only effective ways of feeding people are cultivation and hunting?
Because early humans were not good at math and they liked to eat meat without having to chase it, that's why this ideology doesn't need logic, it's just a tradition. People are used to it therefore they don't care if it's not efficient in any way and only causes damage to themselves and destroys the future of the next generations, by leaving the world in a destroyed state.
Obviously there are some exceptions in history in middle ages the low class lived without eating meat for years, cause being incredibly poor helped them realize how much of a waste of resources it was and they couldn't either hunt cause it was reserved to nobles.
But at any given chance anyone from this poor caste would choose to farm animals.
If your fictional civilizations follows the same traditions and religions as humans with the addiction of animal fighting then it would be perfectly ''plausible'' for them to breed big carnivores just to see them slaughter each other or to bring them to war.
But, I mean they go to war, they are not intelligent enough to care about efficiency in the first place. So probably they would not even need the same traditions and religions of humans.