'Out of Egypt I called my son'
In Hosea the son is Israel; Matthew applies the line to Jesus — typological reading, proof-texting, or both.
Hosea 11:1
1“When Israel was a child, then I loved him, and called my son out of Egypt.
Matthew 2:15
15and was there until the death of Herod; that it might be fulfilled which was spoken by the Lord through the prophet, saying, “Out of Egypt I called my son.”
What each tradition says
Rabbinic / Midrashic
Rashi reads Hosea 11:1 as God saying He called His son from Egypt through His prophets to cleave to His Torah. The comment then asks what they did.
Rashi (R. Shlomo Yitzhaki, 1040-1105), Rashi on Hosea (The Judaica Press complete Tanach with Rashi, trans. A. J. Rosenberg) — Comment on Hosea 11:1
Patristic
Eusebius says the real meaning explains this passage: the Christ is called Israel, as He is in other prophecies. Since He was obedient, He took the form of a servant and became the beloved Son.
Eusebius of Caesarea (c. 260-c. 340), Demonstratio Evangelica (The Proof of the Gospel), trans. W. J. Ferrar (London: SPCK, 1920), Book IX — Book IX, ch. 4 ('From Hosea. Again concerns the Words, Out of Egypt have I Called My Son, and King Herod')
Catholic
Jerome says the Evangelist cites this text because it refers to Christ typically. He observes that in this Prophet and in others, the coming of Christ and the call of the Gentiles are foreshown without breaking the thread of history.
Thomas Aquinas (1225-1274), Catena Aurea, quoting Jerome ('in Osee, 11, 2'), Catena Aurea (Golden Chain), vol. 1: St. Matthew (Oxford translation; London: J. G. F. and J. Rivington, 1842) — On Matthew 2:15 (Jerome's comment on Hosea 11:2, cited in the catena)
Orthodox
Chrysostom answers a Jewish objection that “Out of Egypt I called my Son” was spoken concerning Israel. He replies that this is a law of prophecy: in many cases much that is spoken of one set of persons is fulfilled in another.
John Chrysostom (c. 349-407), Homilies on the Gospel of Saint Matthew, in NPNF ser. 1, vol. 10 (ed. Philip Schaff; New York: Christian Literature Publishing Co., 1886) — Homily VIII, section 5 (on Matthew 2:15)
Reformed / Protestant
Calvin says those not well versed in Scripture have confidently applied this place to Christ, but the context opposes this. He notes scoffers then tried to disturb Christ’s religion, as if the Evangelist had misapplied the prophet. Calvin says the more suitable answer is that there is only a comparison.
John Calvin (1509-1564), Commentaries on the Twelve Minor Prophets, vol. 1: Hosea (trans. John Owen; Edinburgh: Calvin Translation Society, 1846) — Commentary on Hosea 11:1
Evangelical
Barnes suggests the place in Hosea may have become a proverb for any great deliverance from danger, so it could be said to be fulfilled in Christ as proverbs are applied to applicable cases. He holds it cannot be supposed a prophecy of the Messiah; Matthew only used it appropriately to express the event.
Albert Barnes (1798-1870), Notes on the New Testament, Explanatory and Practical (enlarged ed. by Robert Frew; CCEL carries the Baker reprint) — Note on Matthew 2:15