Indeed, animals can't really be evil. They're motivated more by fear or hunger, not by an understanding of their selfishness or of their contempt for their inferiors. So animal tyrannies aren't so absolute or airtight.
In that respect, human ones are worse than animal social hierarchies, since we're more adept at controlling our environment. We have technologies for maximizing our control, including our languages, cultures, and modes of persuasion and of exploitation which cement the clever, ruthless, or more lucky minority's domination of the masses.
What seems to me natural in human societies is our tendency to form social hierarchies for distributing power unequally. The long period of hunter-gatherer equality was perhaps our least natural one, a kind of twilight of childhood innocence for our species. (Or perhaps it was natural or common after all, since we were the prey that had to form herds out of necessity.) As soon as we gained more control over our environment and ourselves, via agriculture and civilization, the hierarchies reemerged.
Whether a revolution is natural or novel and anti-natural would depend on what the rebels are striving to achieve. Animals squabble over the leadership position, whereas the modern political revolutions were individualistic and were about sharing power with the lower social classes or about abolishing hierarchy altogether, as in democracy or communism.
That return to some aspects of hunter-gatherer innocence, mass infantilization and decadence (in place of hunter-gatherer necessity) seems anomalous. We insist we're fighting for our liberation as sovereign individuals, but by pursuing our happiness we become childlike so that our power is illusory. In the wild, power is as obvious as the signals of dominance and submission in the group, or as the predator which hunts and eats the prey.
Western individuals live in a cultural wonderland of spectacles and illusions. It's a samsara or matrix we've created for ourselves that conceals the reality of our self-destructiveness, of the holocaust we've perpetrated against wildlife, and of the damage we've done to the biosphere. In short, modernity is unnatural in various ways. (I haven't even gone into scientific and philosophical enlightenment.)