Dog food: This story, similar in form to that of the healing of a centurion’s servant (8:5-13), is Matthew’s way of further justifying the mission to the Gentiles. Matthew’s community was haunted with a Jesus who claimed to have been “sent only to the lost sheep of the house of Israel.” When Gentiles accepted Jesus and his way, some clarification had to be made regarding the limitations of Jesus’ ministry.
The Canaanite woman addresses Jesus as “Lord, Son of David.” The title “Lord” is used of the risen Christ. The title “Son of David” is used of the triumphant Jesus, who enters the city of Jerusalem to suffer and die.
“O woman, great is your faith!” states Jesus. Matthew attributes Jesus’ granting the woman’s request to her faith. Gentiles believe, too.
A Canaanite, the woman and other Gentiles are referred to as “dogs” by Jesus. She dutifully acknowledges her unworthiness and the privileged position of Israel.
But she uses the derogatory remark to her advantage. The privileged position of Israel is not accessible, but there must be other openings. Surely, the Gentiles can share in the crumbs. In this way, the woman gets a crumb, and her daughter is healed.