2 Abraham begat Isaac; and Isaac begat Jacob; and Jacob begat Judas and his brethren;
[AD 397] Ambrose of Milan on Matthew 1:2
(in Luc. cap. 3. lib. iii. n. 7, 8.) For Abraham was the first who deserved the witness of faith; "He believed God, and it was accounted to him for righteousness." It behoved therefore that he should be set forth as the first in the line of descent, who was the first to deserve the promise of the restoration of the Church, In thee shall all the nations of the earth be blessed. And it is again brought to a period in David, for that Jesus should be called his Son; hence to him is preserved the privilege, that from him should come the beginning of the Lord's genealogy.

[AD 407] John Chrysostom on Matthew 1:2
(Hom. iii.) Matthew then, desiring to preserve in memory the lineage of the Lord's humanity through the succession of His parents, begins with Abraham, saying, Abraham begat Isaac. Why does he not mention lsmael, his first-born? And again, Isaac begat Jacob; why does he not speak of Esau his first-born? Because through them he could not have come down to David.

(Hom. iii.) Or, he names all the twelve Patriarchs that he may lower that pride which is drawn from a line of noble ancestry. For many of these were born of maidservants, and yet were Patriarchs and heads of tribes.

[AD 407] John Chrysostom on Matthew 1:2
Hom. iii, and Aug. City of God, 15, 15: Matthew then, desiring to preserve in memory the lineage of the Lord's humanity through the succession of His parents, begins with Abraham, saying, “Abraham begat Isaac.” Why does he not mention Ismael, his first-born? And again, “Isaac began Jacob;” why does he not speak of Esau his first-born? Because through them he could not have come down to David.
Hom. iii: Or, he names all the twelve Patriarchs that he may lower that pride which is drawn from a line of noble ancestry. For many of these were born of maidservants, and yet were Patriarchs and heads of tribes.
Isaac is interpreted, ‘laughter, 'but the laughter of the saints is not the foolish convulsion of the lips, but the rational joy of the heart, which was the mystery of Christ. For as he was granted to his parents in their extreme age to their great joy, that it might be known that he was not the child of nature, but of grace, thus Christ also in this last time came of a Jewish mother to be the joy of the whole earth; the one of a virgin, the other of a woman past the age, both contrary to the expectation of nature.
Our Jacob in like manner begot the twelve Apostles in the Spirit, not in the flesh; in word, not in blood. Judah is interpreted, ‘confessor,’ for he was a type of Christ who was to be the confessor of His Father, as He spake, “I confess to Thee, Father, Lord of heaven and earth.”
[AD 407] John Chrysostom on Matthew 1:2
But why is it, that having mentioned Abraham, and having said that he begot Isaac, and Isaac, Jacob; and not having made any mention of his brother; when he has come to Jacob, he remembers both Judah, and his brethren? Now there are some that say, it was because of the perverseness of Esau, and of the rest that came before. But I should not say this; for if it were so, how is it that he a little after mentions such women? It being out of contraries, in this place, that His glory is manifested; not by having great forefathers, but low and of little account. For to the lofty One it is a great glory to be able to abase Himself exceedingly. Wherefore then did He not mention them? Because Saracens, and Ishmaelites, and Arabians, and as many as are sprung from those ancestors, have nothing in common with the race of the Israelites. For this cause then he passes over those in silence, and hastens on to His forefathers, and those of the Jewish people. Wherefore he says, And Jacob begot Judas and his brethren. For at this point the race of the Jews begins to have its peculiar mark.
[AD 430] Augustine of Hippo on Matthew 1:2
(De Cons. Evan. ii. 1.) Matthew, by beginning with Christ's genealogy, shows that he has undertaken to relate Christ's birth according to the flesh. But Luke, as rather describing Him as a Priest for the atonement of sin, gives Christ's genealogy not in the beginning of his Gospel, but at His baptism, when John bare that testimony, Lo, He that taketh away the sins of the world. (John 1:29.) In the genealogy of Matthew is figured to us the taking on Him of our sins by the Lord Christ; in the genealogy of Luke, the taking away of our sins by the same; hence Matthew gives them in a descending, Luke in an ascending, series. But Matthew, describing Christ's human generation in descending order, begins his enumeration with Abraham.

[AD 533] Remigius of Rheims on Matthew 1:2
These heresies therefore the Apostles overthrow in the opening of their Gospels, as Matthew in relating how He derived His descent from the kings of the Jews proves Him to have been truly man and to have had true flesh. Likewise Luke, when he describes the priestly stock and person; Mark when he says, The beginning of the Gospel of Jesus Christ the Son of God; and John when lie says, In the beginning was the Word; both show Him to have been before all ages God, with God the Father.

Jacob is interpreted 'supplanter,' and it is said of Christ, Thou hast cast down beneath Me them that rose up against Me. (Ps. 18:43.)

[AD 1107] Theophylact of Ohrid on Matthew 1:2
Matthew begins the genealogy with Abraham because he was the father of the Hebrews, and because he first received the promises that in his seed all the nations would be blessed (Gen. 22:18). Therefore it is fitting that he should give the genealogy of Christ beginning with Abraham, for the seed of Abraham is Christ by Whom all we nations have been blessed who were formerly cursed. "Abraham" means "father of the nations," and "Isaac," "joy" or "laughter." The evangelist makes no mention of the illegitimate children of Abraham, Ishmael and the others, because the Jews were not descended from them, but from Isaac.

You see that he mentioned Judah and his brothers because the twelve tribes were from them.
[AD 1274] Pseudo-Chrysostom on Matthew 1:2
Isaac is interpreted 'laughter,' but the laughter of the saints is not the foolish convulsion of the lips, but the rational joy of the heart, which was the mystery of Christ. For as he was granted to his parents in their extreme age to their great joy, that it might be known that he was not the child of nature, but of grace, thus Christ also in this last time came of a Jewish mother to be the joy of the whole earth; the one of a virgin, the other of a woman past the age, both contrary to the expectation of nature.

Our Jacob in like manner begot the twelve Apostles in the Spirit, not in the flesh; in word, not in blood. Judah is interpreted 'confessor,' for he was a type of Christ who was to be the confessor of His Father, as He spake, I confess to Thee, Father, Lord of heaven and earth.

[AD 1274] Glossa Ordinaria on Matthew 1:2
Yet he names all the brethren of Judah with him in the lineage. lsmael and Esau had not remained in the worship of the true God; but the brethren of Judah were reckoned in God's people.

But Judah is the only one mentioned by name, and that because the Lord was descended from him only. But in each of the Patriarchs we must note not their history only, but the allegorical and moral meaning to be drawn from them; allegory, in seeing whom each of the Fathers foreshewed; moral instruction in that through each one of the Fathers some virtue may be edified in us either through the signification of his name, or through his exampleg. Abraham is in many respects a figure of Christ, and chiefly in his name, which is interpreted the Father of many nations, and Christ is Father of many believers. Abraham moreover went out from his own kindred, and abode in a strange land; in like manner Christ, leaving the Jewish nation, went by His preachers throughout the Gentiles.

Morally; Abraham signifies to us the virtue of faith in Christ, as an example himself, as it is said of him, Abraham believed God, and it was accounted unto Him for righteousness. Isaac may represent hope; for Isaac is interpreted 'laughter,' as he was the joy of his parents; and hope is our joy, making ns to hope for eternal blessings and to joy in them. Abraham begat Isaac, and faith begets hope. Jacob signifies 'love,' for love embraces two lives; active in the love of our neighbour, contemplative in the love of God; the active is signified by Leah, the contemplative by Rachel. For Leah is interpreted. 'labouringh,' for she is active in labour; Racheli 'having seen the beginning,' because by the contemplative, the beginning, that is God, is seen. Jacob is born of two parents, as love is born of faith and hope; for what we believe, we both hope for and love.