Hosea 11:1 looks backward to Israel's history rather than, in its original context, forward to the birth of an individual Messiah: "When Israel was a child, I loved him, and out of Egypt I called my son." Hosea is recalling the Exodus, when God brought the nation He called His son out of Egyptian bondage. This makes the New Testament use of the verse especially important, because the messianic significance is supplied explicitly by Matthew rather than by treating Hosea's historical statement as though it were originally a simple prediction.
Matthew 2:14-15 records Joseph taking Jesus and Mary to Egypt to escape Herod and later returning after Herod's death. Matthew then states directly that this occurred to fulfill the Lord's word through the prophet, "Out of Egypt I called my son." Jesus thus retraces Israel's experience: as Israel, God's son, was called out of Egypt, so Jesus, God's unique Son and representative of Israel, is called out of Egypt. The fulfillment is therefore typological but explicitly authorized by the Gospel itself. Matthew presents Jesus as embodying Israel's story and bringing God's redemptive purpose to its intended fulfillment.