Church Fathers on Matthew 1:2

Matthew, by beginning with Christ’s genealogy, shews 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]

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…

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.