Inequality is baked into the nature of reality. There’s no escaping it anywhere or anytime. Cosmology holds that the universe began in a state of perfect equality but then following the period of rapid expansion (inflation), inequality appeared in the form of clusters of matter (stars and galaxies) and empty space. The primary force that caused that clumping, physicists contend, was gravity. The weakest of all the four forces, gravity molded the universe into the form it has: clumps and voids.
Equality would have implied a structureless universe. Physicists believe that in the far distant future, the universe will end in a heat death. Then everything will be back to the undifferentiated state of pure equality.
On a much smaller scale and in a different domain, we find the same story of increasing inequality. The first single-celled organisms were all the same. Multicellular organisms have greater diversity. The variety of life forms on earth kept increasing through biological evolution.
Diversity and equality are rival properties. The more you have of the one, the less you have of the other. Naturally this is true of the human world since, being part of the universe, we are not exempt from the fundamental laws of the universe.
Life is a Random Draw 