Matthean scholar Ulrich Luz argues that the Gospels, particularly Matthew, should not necessarily be understood as βίος but a whole new genre, “Gospel.” Just as earlier Jewish writers picked up the foundation story and reworked it in there writings, likewise Matthew picked up Mark’s story and reworked it, forming a new foundation story. He says,
Between the biblical-Jewish literature and the Gospels, including the Gospel of the Jewish follower of Jesus, Matthew, the foundation story changes. With his story of Jesus Matthew tells a new foundation story that permits him to understand Israel’s previous foundational text, the Bible, in a completely new light. In my (Luz) judgment, here in the framework of the biblical-Jewish tradition and literary activity something completely new, a revolution, happened.
The ancient church recognized this revolution when it put the title “Gospel” at the head of Matthew’s Jesus story and thus created a new genre designation. In so doign it not only expressed a theological judgment; it also did justice to Matthew’s intention.
Luz, Ulrich. Matthew 1–7. Translated by James E. Crouch. Hermeneia. Minneapolis: Fortress Press, 2007.