11 And inasmuch as it was Matthew's intention to set forth Christ as descending with the object of sharing this mortal state with us, he has mentioned those same generations from Abraham on to Joseph, and on to the birth of Christ Himself, in the form of a descending scale, and at the very beginning of his Gospel. Luke, on the other hand, details those generations not at the commencement of his Gospel, but at the point of Christ's baptism, and gives them not in the descending, but in the ascending order, ascribing to Him preferentially the character of a priest in the expiation of sins, as where the voice from heaven declared Him, and where John himself delivered his testimony in these terms: “Behold the Lamb of God, that takes away the sin of the world!” Besides, in the process by which he traces the genealogy upwards, he passes Abraham and carries us back to God, to whom, purified and atoned for, we are reconciled.
Of merit, too, He has sustained in Himself the origination of our adoption; for we are made the sons of God through adoption, by believing on the Son of God. Moreover, on our account the Son of God was pleased to be made the son of man by the generation which is proper to the flesh. And the evangelist has shown clearly enough that he did not name Joseph the son of Heli on the ground that he was begotten of him, but only on the ground that he was adopted by him. For he has spoken of Adam also as the son of God, who, strictly speaking, was made by God, but was also, as it may be said, constituted a son in paradise by the grace which afterwards he lost through his transgression.
Source: The Harmony of the Gospels (New Advent)