It is from a mistranslation of Romans 5 in the Latin, as Jaroslav Pelikan observes with regard to Augustine (though Augustine was not the only major Latin-speaking to writer to be influenced by it; cf also any major critical commentary on Romans):
"In Augustine's Latin Bible Romans 5:12 read "Sin came into the world, and death through sin, and so death spread to all men, through one man in whom all men sinned [in quo omnes peccaverunt]." Although this last clause really meant "because [ἐφ’ ᾧ] all men sinned," the translation "in whom all men sinned" had lead an earlier Western theologian to conclude that "all have sinned in Adam, as it were in the mass, for he himself was corrupted by sin, and all whom he begot were born under sin" (Ambrosiast Rom 5.12.3). Quoting these words, Augustine insisted that "all men are understood to have sinned in the first man, because all men were in him when he sinned" (Pelag 4.4.7). Just how they were in Adam, he usually explained by referring to the "carnal begetting" (Augustine, Pecc Merit 1.15.19) by which their lives began. For "by the begetting of the flesh... that sin is contracted which is original" (Pecc Merit 1.15.20as distinguished from that which a man committed himself. Sin and death had been transmitted to all men from one man "by the propagation of the human race" (Pecc Merit 1.9.10). A variant reading of Luke 20:34, "The sons of the age beget and are begotten," meant that even Christian parents begot "sons of this present age" (Nupt et concup 1.18.20) who were born of the lust of the flesh and to whom its contagion was passed on. Because it was transmitted by natural propagation, original sin was as universal and inevitable as life itself. "Behold," wrote Augustine in summary, "what harm the disobedience of the will has inflicted on human nature! Let him be permitted to pray that he may be healed [orare sinutar, ut sinutar]. Why should he presume so much on the capacity of his nature? It is wounded, hurt, damaged, destroyed. It needs a true confession, not a false defense; it needs the grace of God, not that it may be created, but that it may be restored" (Augustine, Nat et grat 53.62]. The use of such a term as "destroyed" rather than only "damaged" to describe human nature after the fall of Adam could lead to the impression that as a result of sin man had ceased being man and was now being created, at least partly, in the image of the devil rather than in the image of God. Such had been Augustine's personal belief during the nearly nine years that he was a Manichean (Augustine, Conf 3.6.11; 3.11.20). For the Manicheans had taught that the begetting of men took place in "madness and intemperance" of sexual lust and that therefore it was blasphemous to suppose that "God forms us according to his own image" through the madness and lust of our parents (Augustine, Faust 26.1). Augustine's theory of the transmission of sin from generation to generation through carnal begetting, as though this were some sort of venereal disease, seemed suspiciously reminiscent of the Manichean doctrine, enough so to prompt the charge of one of his contemporaries that "anyone who defends [the doctrine of] original evil is thoroughgoing Manichaean" (apAug Nupt et concup 2.29.49). For Augustine as an orthodox Christian, the image of God had not been lost through the fall and man had not ceased being God's good creature: God created man according to his image, "not as regards the possession of a body and of physical life, but as regards the possession of a rational mind by which to know God." He distinguished his view of innate and radical evil from the Manichean by holding two doctrines together which the Manicheans (as well as the Pelagians) treated as mutually contradictory. Man had "a good creation but a corrupt propagation, confessing for his goods a most excellent Creator and seeking for his evils a most merciful Redeemer" (Aug Pelag 4.4.4). The nature of man as a creature of God remained even after the fall into sin, which as a turning away from God to evil did not mean the creation of another and evil nature but the corruption of that nature which had already been created good; for "although there was a fault present in nature, yet nature was not itself a fault" (Grat Christ 19.20; Nat et grat 3.3). It still possessed life, senses, and intellect as gifts of the Creator. And therefore man was neither created in the image of the devil nor degraded to the level of the brutes. "For man has such excellence [even after the fall] in comparison with the brute that what is a fault in man is nature in the brute. Still man's nature is not changed into the nature of the brute. God therefore condemns man because of the fault by which his nature is discraced, not because of his nature, which is not abolished through his fault" (Aug Pecc orig 40.46). Nature had not been destroyed, but it had been gravely wounded and needed to be healed by divine grace which had been lost in the fall but was now restored in Christ. Grace was more than nature, more than free will, more than even the forgiveness of sins and the gift of God's commandments; it was the divinely given power to avoid and conquer sin" (Gest Pelag 31.56; Ep 177.4). -From Jaroslav Pelikan, The Christian Tradition: A History of the Development of Doctrine, Vol 1: The Emergence of the Catholic Tradition (Chicago: University of Chicago Press), pp. 299-301.
Augustine's acumen as a former pagan philosopher is also widely thought to have come into play, regarding which I'll include a few additional remarks of interest...
Pelikan also gives credence to "the possibility that Augustine's doctrine of grace is merely a consequence of his NeoPlatonism, and of the concept of God that emerged from this, in which the idea of absolute causality and omnipotence is raised to a position of greater importance than the Father's love. Especially in his earlier writings Augustine seemed to identify the biblical doctrine of God as Creator with "what Plato and Plotinus have said about God" (Augustine, Soliloq 1.4.9). He himself quoted Simplicanus, one of his early mentors in the gospel, as advising him that "in the Platonists, at every turn, the pathway led to belief in God and in his word" (Augustine, Conf 8.2.3). On the basis of these earlier writings it has been claimed that "morally as well as intellectually, he was converted to NeoPlatonism rather than the gospel" (Alfaric 1:399). It is appropriate here to observe how consistently Platonic was Augustine's early doctrine of knowledge of the soul, which identified the work of Christ as the divine teacher with the idea of recollection (anamnesis), so that "we do not consult a speaker who utters sounds to the outside, but a truth that presides within... Christ, who is said to dwell in the inner man -he it is who teaches" (Aug Mag 38). It would require only "the change of a few words and sentiments" for Plato and his followers to become Christians" (Aug, Vera Relig 4.7). (Pelikan, op cit, p. 295).
"When he came to speak of the divine essence it was usually defined in relation to absoluteness and impassibility rather than on the basis of the active involvement of God in creation and redemption [contrast also the Cappadocians for whom the divine essence was unknowable and inconceivable, a position retained in Orthodoxy from earlier centuries to the present]. ...Book 4 of On the Trinity was given over to an extensive dissertation on the saving effect of the incarnation and death of Christ. But even this was connected to the preceding book by the statement that "the essence of God by which he is, has nothing changeable" in it (Aug, Trin 4 pr), and was connected to the following book by the declaration that "he who is God is the only unchangeable substance or essence to whom certainly being itself [ipsum esse], from which the noun 'essence' comes, most especially and truly belongs" (Aug Trin 5.2.3). The dogma of the Trinity and the drama of redemption must be interpreted in a manner that would be consistent with this a priori definition of the deity of God. Neoplatonic elements were unmistakably present in this definition, but in setting it forth Augustine believed himself to be -and he was- expressing the catholic creed. What was distinctive about his version of that creed was his awareness of the sovereignty of divine power and divine grace. This awareness took the form of a doctrine of predestination more thoroughgoing than that of any major orthodox thinker since Paul. He defined predestination as "God's arrangement of his future works in his prescience, which cannot be deceived and changed." ...Since grace was sovereign, those whom God had predestined would be saved... Why then did God create those who fall he foreknew? To manifest his wrath and to demonstrate his power... double predestination applied not only to the city of God and the city of earth, but also to individuals. Some were predestined to eternal life, others to eternal death; and among these latter were infants who died without baptism..." (Pelikan, op cit, pp. 295-298).