12 When one reflects on the origin of this doctrine, there come to mind at once the words of the Apostle: "Where sin abounded, grace did more abound." All know that the father of the whole human race was constituted by God in so exalted a state that he was to hand on to his posterity, together with earthly existence, the heavenly life of divine grace. But after the unhappy fall of Adam, the whole human race, infected by the hereditary stain, lost their participation in the divine nature, and we were all "children of wrath." But the all-merciful God "so loved the world as to give His only-begotten Son," and the Word of the Eternal Father with the same divine love assumed human nature from the race of Adam - but as an innocent and spotless nature - so that He, as the new Adam, might be the source whence the grace of the Holy Spirit should flow unto all the children of the first parent. Through the sin of the first man they had been excluded from adoption as children of God; through the Word incarnate, made brothers according to the flesh of the only-begotten Son of God, they receive also the power to become the sons of God. As He hung upon the Cross, Christ Jesus not only appeased the justice of the Eternal Father which had been violated, but He also won for us, His brethren, an ineffable flow of graces. It was possible for Him of Himself to impart these graces to mankind directly; but He willed to do so only through a visible Church made up of men, so that through her all might cooperate with Him in dispensing the graces of Redemption. As the Word of God willed to make use of our nature, when in excruciating agony He would redeem mankind, so in the same way throughout the centuries He makes use of the Church that the work begun might endure.
Source: Mystici Corporis Christi (Vatican.va)