Here it ought to be considered...that two Evangelists describe Christ’s generation according to the flesh in detail, namely, Luke and Matthew; but they describe it differently. And this difference is observed in regard to five things. For, firstly, they differ so far as regards the position; secondly, they differ as regards the order; thirdly, they differ as regards the manner; fourthly, they differ as regards the terminus; fifthly, they differ as regards the persons enumerated. Firstly, I say that they differ regarding the position: because Matthew starts to trace Christ’s generation in the beginning of the Gospel; Luke, however, starts to trace Christ’s generation not in the beginning, but after His baptism: and the reason is, according to Augustine, that Matthew received the obligation of describing Christ’s carnal generation; and, for that reason, he ought to put it immediately at the beginning; Luke, however, especially intended to praise the priestly person in Christ; now to the priest pertains the expiation of sins. And, for that reason, after the baptism, in which the expiation of sins occurs, Christ’s generation is conveniently placed by Luke. Now, secondly, Luke and Matthew in tracing Christ’s genealogy differ regarding the order: because Matthew traces Christ’s generation by beginning from Abraham, and descending all the way to Christ; Luke, however, begins from Christ, and, by ascending, proceeds all the way to Abraham and even further. And the reason is that, according to the Apostle (Rom. 4, 25), 8 in Christ there were two things, namely, His humility in accepting the defects of our nature, and the power of His divinity and grace, through which He made atonement for us from these defects; “God sent his own Son in the likeness of sinful flesh” (on account of the first), “and of sin, hath condemned sin in the flesh” (on account of the second)” (Rom. 8, 3). Matthew, therefore, who stressed Christ’s carnal generation, through which He descended even to the assumption of our infirmity, fittingly wrote out His generation by descending. But Luke, who commended the priestly dignity in Him, through which we are reconciled to God and united to Christ, fittingly proceeds by ascending. Thirdly, they differ regarding the manner: because in the detailed exposition of the genealogy, Matthew uses the word begot, but Luke uses the word “was”: and this is because Matthew, in his whole detailed exposition, gives the ancestors according only to the flesh; but Luke gives many ancestors according to the Law, or by adoption. For it was commanded in the Law that if someone were to die without children, that his brother would take his wife, and beget sons unto him: hence, those sons did not belong to him who begot them; but through a kind of adoption they were imputed to the former. Hence, Luke, who gives many sons begotten through adoption, does not say begot, but “was”; because although they had not begotten them, nevertheless, they were theirs through a kind of adoption. Matthew, however, who gives only the ancestors according to the flesh, says, begot. However, the reason for this is that, as it was said, Matthew’s aim is chiefly directed towards Christ’s humanity. And because He was born from the ancestors according to the flesh, for that reason, in Matthew’s genealogy no one is set down who will not have been an ancestor according to the flesh. Luke, however, chiefly commends the priestly dignity in Christ, through which we are adopted as sons of God; and therefore, he set down not only the ancestors according to the flesh, but also the legal ancestors. Fourthly, they differ regarding the terminus, because Matthew starts his parentage from Abraham, and it is continued even unto Christ; Luke, however, starts from Christ, and his parentage is continued not only unto Abraham, but even unto God. The reason for this can be taken from the fact that Matthew wrote for the Hebrews; now the Hebrews were especially taking pride in Abraham; “We are the seed of Abraham” (Jn. 8, 33), who was the first principle of believing; and therefore Matthew started from Abraham. Luke, however, wrote for the Greeks, who knew nothing about Abraham, except in reference to Christ: for if Christ had not existed, they would have never known anything about Abraham; and therefore, Luke began from Christ and ended not only with Abraham, but with God. Fifthly, they differ regarding the persons enumerated: because in Luke’s entire genealogical lineage there is absolutely no mention of a woman; in Matthew’s, however, some women are interspersed. The reason for this is, according to Ambrose, that Luke, as it was said, especially commended the priestly dignity; in a priest, however, purity is especially required. Matthew, however, traced His generation according to the flesh: and therefore some women are placed therein. Nevertheless, one ought to observe that in Matthew’s entire genealogy only sinful women are put down, or rather women who were known to have been in some sin, such as Thamar, who was an fornicator (Gen. 38); and Ruth, who was an idolatress, because she was a Gentile: and the wife of Urias, who was an adulteress (II Kings 11). And this was for the purpose of signifying, according to Jerome, that He, whose genealogy is traced, came into this world for the sake of redeeming sinners. Another reason is mentioned by Ambrose, namely, the sinful women were included so that the Church’s embarrassment might be taken away. For if Christ willed to be born of sinners, then infidels ought not to mock, if sinners come into the Church. Another reason can be assigned, I believe it is according to Chrysostom, that the imperfection of the Law might be shown: and that Christ came to fulfill the Law. For by the fact that certain sinful women are mentioned, it is denoted that they, who were greatest in relation to the Law, were sinners; such as David and Juda; and in this he indicates the imperfection of the others. For if these were sinners, much more others were sinners also; “All have sinned and do need the glory of God” (Rom. 3, 23). And, therefore, these are put down in Christ’s generation, so that it might be signified that He had fulfilled the Law. Observe, nevertheless, that these women, although they all were sinners, nevertheless, were not sinners at the time when their genealogy is traced; but had been by then cleansed by penance.

Aquinas, St. Thomas  (2012-02-06). Commentary on the Gospel of St. Matthew (p. 12-14). Dolorosa Press. Kindle Edition.