Antinatalism, or anti-natalism, is a philosophical position and social movement that assigns a negative value to birth. Antinatalists argue that humans should abstain from procreation because it is morally wrong (some also recognize the procreation of other sentient beings as morally wrong) — Wikipedia

The term antinatalism is in opposition to the term natalism or pro-natalism, and was used probably for the first time as the name of the position by Théophile de Giraud in his book L'art de guillotiner les procréateurs: Manifeste anti-nataliste — Wikipedia

Théophile de Giraud

The discoverer of the causative agent of leprosy also known as Hansen's disease was Gerhard Armauer Hansen

Renowned orthopedist and missionary to lepers, Dr. Paul Brand explains that leprosy attacks the nerve cells that feel pain resulting in no more pain for the leper, which leads to ever increasing, often catastrophic, damage to the body of the leper — Wikipedia

Dr. Paul Brand

The basic idea is that pain is essential for survival, without it we would all be dead. In other words, an antinatalist's demand that for life to be worth living there should be no pain would lead to extinction of all life for we wouldn't be able to protect ourselves from injuries, minor ones becoming aggravated to the point of being lethal, forget about major injuries.

This post covers some ground in theodicy too. Please feel free to explore the links.

The paradox for antinatalism is that their condition for life (the absence of pain) amounts to a death sentence for all life. Life (is?) seems impossible without pain.