Augustine of Hippo built the developed doctrine of original sin during a running fight with Pelagius, a British monk teaching in Rome around 400 CE who held that Adam's sin harmed only Adam, leaving every later person born morally neutral and fully capable of choosing good without special grace. Augustine, most fully in On Nature and Grace, answered that Adam's guilt is transmitted to the whole human race, so that every infant is born already guilty and in need of the grace baptism confers, not merely bad example to be resisted by will.
One text carried unusual weight in the argument. The Latin Vulgate rendered Romans 5:12 as saying death spread to all because in whom, in quo, all sinned, read as all humanity sinning covertly in Adam himself. The Greek behind it, eph ho, more naturally means because or in that all sinned, describing each person's own sin as the cause of death rather than participation in Adam's single act. Augustine, who read Paul in Latin and had limited Greek, leaned on the stronger reading the mistranslation supplied.
The Council of Carthage condemned Pelagius's teaching in 418 and the Western church followed Augustine's account, formalized centuries later at the Council of Trent and still confessed in the Catholic Catechism. Eastern Christianity took a different route from the same starting texts, holding that Adam's sin left humanity mortal and disordered without holding each descendant personally guilty of Adam's own act, a distinction Orthodox theology has pressed as the real fault line between the two halves of the old empire's church.