Objection 1. It would seem that Christ's genealogy is not suitably traced by the Evangelists. For it is written (Isaiah 53:8): "Who shall declare His generation?" Therefore Christ's genealogy should not have been set down.
Objection 2. Further, one man cannot possibly have two fathers. But Matthew says that "Jacob begot Joseph, the husband of Mary": whereas Luke says that Joseph was the son of Heli. Therefore they contradict one another.
Objection 3. Further, there seem to be divergencies between them on several points. For Matthew, at the commencement of his book, beginning from Abraham and coming down to Joseph, enumerates forty-two generations. Whereas Luke sets down Christ's genealogy after His Baptism, and beginning from Christ traces the series of generations back to God, counting in all seventy-seven generations, the first and last included. It seems therefore that their accounts of Christ's genealogy do not agree.
Objection 4. Further, we read (2 Kings 8:24) that Joram begot Ochozias, who was succeeded by his son Joas: who was succeeded by his son Amasius: after whom reigned his son Azarias, called Ozias; who was succeeded by his son Joathan. But Matthew says that Joram begot Ozias. Therefore it seems that his account of Christ's genealogy is unsuitable, since he omits three kings in the middle thereof.
Objection 5. Further, all those who are mentioned in Christ's genealogy had both a father and a mother, and many of them had brothers also. Now in Christ's genealogy Matthew mentions only three mothers--namely, Thamar, Ruth, and the wife of Urias. He also mentions the brothers of Judas and Jechonias, and also Phares and Zara. But Luke mentions none of these. Therefore the evangelists seem to have described the genealogy of Christ in an unsuitable manner.
On the contrary, The authority of Scripture suffices.
I answer that, As is written (2 Timothy 3:16), "All Holy Scripture is inspired of God [Vulgate: 'All scripture inspired of God is profitable', etc. Now what is done by God is done in perfect order, according to Romans 13:1: "Those that are of God are ordained [Vulgate: 'Those that are, are ordained of God']. Therefore Christ's genealogy is set down by the evangelists in a suitable order.
Reply to Objection 1. As Jerome says on Matthew 1, Isaias speaks of the generation of Christ's Godhead. Whereas Matthew relates the generation of Christ in His humanity; not indeed by explaining the manner of Incarnation, which is also unspeakable; but by enumerating Christ's forefathers from whom He was descended according to the flesh.
Reply to Objection 2. Various answers have been made by certain writers to this objection which was raised by Julian the Apostate; for some, as Gregory of Nazianzum, say that the people mentioned by the two evangelists are the same, but under different names, as though they each had two. But this will not stand: because Matthew mentions one of David's sons--namely, Solomon; whereas Luke mentions another--namely, Nathan, who according to the history of the kings (2 Samuel 5:14) were clearly brothers.
Wherefore others said that Matthew gave the true genealogy of Christ: while Luke gave the supposititious genealogy; hence he began: "Being (as it was supposed) the son of Joseph." For among the Jews there were some who believed that, on account of the crimes of the kings of Juda, Christ would be born of the family of David, not through the kings, but through some other line of private individuals.
Others again have supposed that Matthew gave the forefathers according to the flesh: whereas Luke gave these according to the spirit, that is, righteous men, who are called (Christ's) forefathers by likeness of virtue.
But an answer is given in the Qq. Vet. et Nov. Test. [Part i, qu. lvi; part 2, qu. vi] to the effect that we are not to understand that Joseph is said by Luke to be the son of Heli: but that at the time of Christ, Heli and Joseph were differently descended from David. Hence Christ is said to have been supposed to be the son of Joseph, and also to have been the son of Heli as though (the Evangelist) were to say that Christ, from the fact that He was the son of Joseph, could be called the son of Heli and of all those who were descended from David; as the Apostle says (Romans 9:5): "Of whom" (viz. the Jews) "is Christ according to the flesh."
Augustine again gives three solutions (De Qq. Evang. ii), saying: "There are three motives by one or other of which the evangelist was guided. For either one evangelist mentions Joseph's father of whom he was begotten; whilst the other gives either his maternal grandfather or some other of his later forefathers; or one was Joseph's natural father: the other is father by adoption. Or, according to the Jewish custom, one of those having died without children, a near relation of his married his wife, the son born of the latter union being reckoned as the son of the former": which is a kind of legal adoption, as Augustine himself says (De Consensu Evang. ii, Cf. Retract. ii).
This last motive is the truest: Jerome also gives it commenting on Matthew 1:16; and Eusebius of Caesarea in his Church history (I, vii), says that it is given by Africanus the historian. For these writers says that Mathan and Melchi, at different times, each begot a son of one and the same wife, named Estha. For Mathan, who traced his descent through Solomon, had married her first, and died, leaving one son, whose name was Jacob: and after his death, as the law did not forbid his widow to remarry, Melchi, who traced his descent through Mathan, being of the same tribe though not of the same family as Mathan, married his widow, who bore him a son, called Heli; so that Jacob and Heli were uterine brothers born to different fathers. Now one of these, Jacob, on his brother Heli dying without issue, married the latter's widow, according to the prescription of the law, of whom he had a son, Joseph, who by nature was his own son, but by law was accounted the son of Heli. Wherefore Matthew says "Jacob begot Joseph": whereas Luke, who was giving the legal genealogy, speaks of no one as begetting.
And although Damascene (De Fide Orth. iv) says that the Blessed Virgin Mary was connected with Joseph in as far as Heli was accounted as his father, for he says that she was descended from Melchi: yet must we also believe that she was in some way descended from Solomon through those patriarchs enumerated by Matthew, who is said to have set down Christ's genealogy according to the flesh; and all the more since Ambrose states that Christ was of the seed of Jechonias.
Reply to Objection 3. According to Augustine (De Consensu Evang. ii) "Matthew purposed to delineate the royal personality of Christ; Luke the priestly personality: so that in Matthew's genealogy is signified the assumption of our sins by our Lord Jesus Christ": inasmuch as by his carnal origin "He assumed 'the likeness of sinful flesh.' But in Luke's genealogy the washing away of our sins is signified," which is effected by Christ's sacrifice. "For which reason Matthew traces the generations downwards, Luke upwards." For the same reason too "Matthew descends from David through Solomon, in whose mother David sinned; whereas Luke ascends to David through Nathan, through whose namesake, the prophet, God expiated his sin." And hence it is also that, because "Matthew wished to signify that Christ had condescended to our mortal nature, he set down the genealogy of Christ at the very outset of his Gospel, beginning with Abraham and descending to Joseph and the birth of Christ Himself. Luke, on the contrary, sets forth Christ's genealogy not at the outset, but after Christ's Baptism, and not in the descending but in the ascending order: as though giving prominence to the office of the priest in expiating our sins, to which John bore witness, saying: 'Behold Him who taketh away the sin of the world.' And in the ascending order, he passes Abraham and continues up to God, to whom we are reconciled by cleansing and expiating. With reason too he follows the origin of adoption; because by adoption we become children of God: whereas by carnal generation the Son of God became the Son of Man. Moreover he shows sufficiently that he does not say that Joseph was the son of Heli as though begotten by him, but because he was adopted by him, since he says that Adam was the son of God, inasmuch as he was created by God."
Again, the number forty pertains to the time of our present life: because of the four parts of the world in which we pass this mortal life under the rule of Christ. And forty is the product of four multiplied by ten: while ten is the sum of the numbers from one to four. The number ten may also refer to the decalogue; and the number four to the present life; or again to the four Gospels, according to which Christ reigns in us. And thus "Matthew, putting forward the royal personality of Christ, enumerates forty persons not counting Him" (cf. Augustine, De Consensu Evang. ii). But this is to be taken on the supposition that it be the same Jechonias at the end of the second, and at the commencement of the third series of fourteen, as Augustine understands it. According to him this was done in order to signify "that under Jechonias there was a certain defection to strange nations during the Babylonian captivity; which also foreshadowed the fact that Christ would pass from the Jews to the Gentiles."
On the other hand, Jerome (on Matthew 1:12-15) says that there were two Joachims--that is, Jechonias, father and son: both of whom are mentioned in Christ's genealogy, so as to make clear the distinction of the generations, which the evangelist divides into three series of fourteen; which amounts in all to forty-two persons. Which number may also be applied to the Holy Church: for it is the product of six, which signifies the labor of the present life, and seven, which signifies the rest of the life to come: for six times seven are forty-two. The number fourteen, which is the sum of ten and four, can also be given the same signification as that given to the number forty, which is the product of the same numbers by multiplication.
But the number used by Luke in Christ's genealogy signifies the generality of sins. "For the number ten is shown in the ten precepts of the Law to be the number of righteousness. Now, to sin is to go beyond the restriction of the Law. And eleven is the number beyond ten." And seven signifies universality: because "universal time is involved in seven days." Now seven times eleven are seventy-seven: so that this number signifies the generality of sins which are taken away by Christ.
Reply to Objection 4. As Jerome says on Matthew 1:8-11: "Because Joram allied himself with the family of the most wicked Jezabel, therefore his memory is omitted down to the third generation, lest it should be inserted among the holy predecessors of the Nativity." Hence as Chrysostom [Cf. Opus Imperf. in Matth. Hom. i, falsely ascribed to Chrysostom] says: "Just as great was the blessing conferred on Jehu, who wrought vengeance on the house of Achab and Jezabel, so also great was the curse on the house of Joram, through the wicked daughter of Achab and Jezabel, so that until the fourth generation his posterity is cut off from the number of kings, according to Exodus 20:5: I shall visit [Vulgate: 'Visiting'] the iniquity of the fathers upon the children unto the third and fourth generations."
It must also be observed that there were other kings who sinned and are mentioned in Christ's genealogy: but their impiety was not continuous. For, as it is stated in the book De Qq. Vet. et Nov. Test. qu. lxxxv: "Solomon through his father's merits is included in the series of kings; and Roboam... through the merits of Asa," who was son of his (Roboam's) son, Abiam. "But the impiety of those three [i.e. Ochozias, Joas, and Amasias, of whom St. Augustine asks in this question lxxxv, why they were omitted by St. Matthew] was continuous."
Reply to Objection 5. As Jerome says on Matthew 1:3: "None of the holy women are mentioned in the Saviour's genealogy, but only those whom Scripture censures, so that He who came for the sake of sinners, by being born of sinners, might blot out all sin." Thus Thamar is mentioned, who is censured for her sin with her father-in-law; Rahab who was a whore; Ruth who was a foreigner; and Bethsabee, the wife of Urias, who was an adulteress. The last, however, is not mentioned by name, but is designated through her husband; both on account of his sin, for he was cognizant of the adultery and murder; and further in order that, by mentioning the husband by name, David's sin might be recalled. And because Luke purposes to delineate Christ as the expiator of our sins, he makes no mention of these women. But he does mention Juda's brethren, in order to show that they belong to God's people: whereas Ismael, the brother of Isaac, and Esau, Jacob's brother, were cut off from God's people, and for this reason are not mentioned in Christ's genealogy. Another motive was to show the emptiness of pride of birth: for many of Juda's brethren were born of hand-maidens, and yet all were patriarchs and heads of tribes. Phares and Zara are mentioned together, because, as Ambrose says on Luke 3:23, "they are the type of the twofold life of man: one, according to the Law," signified by Zara; "the other by Faith," of which Phares is the type. The brethren of Jechonias are included, because they all reigned at various times: which was not the case with other kings: or, again, because they were alike in wickedness and misfortune.
Source: Summa Theologica (New Advent)