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.