Read the first few chapters of Matthew, and take note of the Old Testament prophecies he cites. When Matthew cites Micah 5:2, the meaning is very clear. God made a predictive prophecy about where the Messiah would be born, and that prophecy is fulfilled when Jesus is born in that exact town. But that’s not the only thing “fulfill” means here.
Consider “Out of Egypt I called My son.” The son in question in Hosea 11 is Israel—not just the man Jacob (although he’s included) but the whole nation that came from him. “When Israel was a child I loved him” might refer to the man Jacob, but “out of Egypt I called My son” can’t mean just that one guy, because that guy died in Egypt, and what was called out of Egypt was not that one man, but all his descendants, 400 years later. So “Out of Egypt I called My son” is the utterance of a prophet, but it’s not a predictive prophecy; it’s a comment on Israel’s history. In what sense can it be “fulfilled”?
In order to grasp Matthew’s point here, we must first pay careful attention to the meaning of Hosea. Knowing that Israel is God’s son, Matthew shows how Jesus walks in the steps of Israel. He’s making two points: first, that Jesus is Israel (in a meaningful sense that Matthew will spend the whole book exploring), and second, that the land of Israel has become spiritual Egypt—a point that would be reinforced by John the Baptist when he calls the remnant out into the desert to pass through water. Jesus adds to Hosea; we can’t read Hosea 11 anymore without also thinking of Jesus’ flight from Herod as well as the Exodus. The words of the prophet have been “fulfilled,” made more full than they were before.
We don’t want to read something into the text that isn’t there. At the same time, we don’t want to miss something that is there—and the New Testament writers show us repeatedly that there’s a lot more there than one might think at first glance. From Jesus Himself proving the resurrection by exegeting a verb tense in Genesis to the fulfillments of the first few chapters of Matthew to the dizzying displays of Hebrews, the New Testament authors show us a way of reading the Old Testament that we wouldn’t have come up with on our own. It had to be revealed to us.
In theologically conservative circles, we have gotten our hermeneutics from the Book of Nature (mostly as read by E. D. Hirsch), which is very useful as far as it goes. But there’s two books, and the Book of Scripture also has something to teach us about how to read. We should read both books.