People need to believe they have equal social and political rights, else there would be mass protests, revolutions and anarchy. Whether they actually exist in real life is irrelevant here, only the belief matters.
The primary difference in the social structures of humans and animals is the forced imposition of order in human society, leading to a more 'collective' society, instead of the usual 'survival of the fittest/law of the jungle' structure.
And the concept of equal rights is necessary to achieve this imposition of order.
In my opinion, a human society following 'law of the jungle' would be unsustainable, simply because humans as a species are too weak to survive as individuals. The greatest strength of our species is our mental faculty. This leads to the sum of the parts being greater than the whole. As individuals though, we would fail to harness this strength.
Therefore, equal rights do offer us an evolutionary advantage, since they allow us to cluster together, and grow as a population, which is the only way for us to survive.
To this awnser it is false
