The first verse of Matthew’s Gospel identifies Jesus as “the son of David, the son of Abraham.” Compared to his Davidic pedigree, Jesus as “son of Abraham” has until recently been relatively neglected. Leroy Huizenga’s 2009 book The New Isaac was a tremendous leap forward for appreciating Matthew’s presentation of Jesus as “son of Abraham.”
Huizenga cogently urges that we should accord significant weight to the title “son of Abraham” in Matt. 1:1 (see esp. pp. 139–43), and he goes to on mount an impressive case that the angel’s speech to Joseph in Matthew 1:20–21 alludes to God’s words to Abraham in Genesis 17:19 (pp. 144–51). Joseph the “righteous” (Matt. 1:19) corresponds to Abraham, who is known for his “righteousness” (Gen. 15:6; 18:19; 24:27); Mary the Virgin corresponds to Sarah the barren; and the miraculous birth of Jesus matches—indeed, outmatches—the miraculous birth of Isaac.
Huizenga’s next stop in his explication of the Jesus-Isaac typology is the Lord’s baptism, where the Father identifies Jesus as “my beloved Son” (ho huios mou ho agapētos, Matt. 3:17), which matches the description of Isaac in Genesis 22 LXX. There is much more to Huizenga’s vigorous and persuasive exposition of the significance of Isaac typology in Matthew’s presentation of Jesus—the book is highly recommended.
I’d like to offer a small addendum to Huizenga’s case for Isaac typology in these early chapters of Matthew. In Matthew 3:9, John the Baptist inveighs against the Pharisees and Sadducees, warning them “not [to] presume to say to yourselves, ‘We have Abraham as our father,’ for I tell you, God is able from these stones to raise up children for Abraham” (ESV-CE).
There is a lot going on in this evocative verse. For one thing, as Huizenga notes,
John’s words of caution regarding Abrahamic sonship may be of import and provide a point of contrast: whereas the Pharisees and Sadducees presume Abrahamic sonship (3:9) but are disobedient (3:7–8), Jesus is presented by the heavenly voice as the beloved Son, implying to the Model Reader that he will be the obedient Son of Abraham, like the Isaac of the Akedah…New Isaac, p. 174
I think this is right, but I also think the allusion to Isaac is even stronger. Some commentators have noted that the reference to “children for Abraham” coming from “stones” is reminiscent of Isaiah 51:1–2:
Listen to me, you who pursue righteousness, you who seek the Lord:(ESV-CE)
look to the rock from which you were hewn,
and to the quarry from which you were dug.
Look to Abraham your father
and to Sarah who bore you;
for he was but one when I called him,
that I might bless him and multiply him.
Picking up on this allusion, the attentive reader will notice a dramatic irony. Not only is God able to raise up children for Abraham from “these stones,” he already has raised up a “son of Abraham” (Matt. 1:1) from the “stones” of a celibate couple (1:25) who are compared to Abraham and Sarah (1:20–21).
Two further considerations seem to lend support to the possibility of an Isaac reference in Matthew 3:9. First, the scene that immediately follows is Jesus’ baptism, which, as noted above, contains a clear allusion to the Aqedah in Genesis 22. Second, the immediately preceding context of 3:9 also subtly reminds the reader of the Jesus-Isaac typology. In 3:6, we read that the people “were baptized by [John] in the river Jordan, confessing their sins” (ESV-CE). This is the first mention of “sin(s)” since 1:21, where Joseph learned he was to name Mary’s child “Jesus, for he will save his people from their sins” (ESV-CE). And Matt. 1:20–21, you’ll recall, alludes to the promise of Isaac’s birth in Genesis 17.
I don’t think Isaac typology is the only meaning Matthew wants readers to draw out of the reference to God being “able from these stones to raise up children for Abraham.” But I do think it’s one of them, and it offers yet one more piece of evidence that we do well to attend carefully to the significance of Jesus as new Isaac.
 It is worth noting, however, that Huizenga shows that Jesus-Isaac typology was not lost on the Fathers of the Church.
 See also Patrick Schreiner, Matthew, Disciple and Scribe: The First Gospel and Its Portrait of Jesus, pp. 215–16.
 E.g., Davies and Allison, Matthew 1–7, pp. 308–309; R. T. France, The Gospel of Matthew, p. 112. As Davies and Allison note, the connection between Matt. 3:9 and Isa. 51:1–2 was already noticed by St John Chrysostom. See Homily on Matthew 11.3.