What the Bible says
“Have mercy on me, O Lord, thou Son of David; my daughter is grievously vexed with a devil.”
Matthew 15:22 (KJV)
“It is not meet to take the children's bread, and to cast it to dogs. And she said, Truth, Lord: yet the dogs eat of the crumbs which fall from their masters' table.”
Matthew 15:26–27 (KJV)
“O woman, great is thy faith: be it unto thee even as thou wilt. And her daughter was made whole from that very hour.”
Matthew 15:28 (KJV)
A household picture
The word Jesus used is a small, household dog — the kind that waits under the family table — not a wild street dog. He was describing the order of his mission: first to the lost sheep of the house of Israel (Matthew 15:24), and then to the nations.
Faith that would not let go
She was a Gentile, a woman, and a stranger, and the disciples wanted her sent away. Yet she called him Lord and Son of David, knelt, and answered his picture with humble, quick-witted faith. She did not ask for the children's place; she asked only for crumbs, because she knew even a crumb from him would be enough.
The point of the story
Matthew places this story right after Jesus teaches that what defiles a person comes from the heart, not from outward things. A Gentile mother walks away with her prayer answered and her faith praised. The door Jesus seemed to close was the door he opened for all the nations.
Common questions
Was Jesus being cruel to the Canaanite woman?
No. He spoke of a household pet under the table, tested and drew out her faith, and ended by praising it and healing her daughter.
Why did Jesus say he was sent only to Israel?
His earthly ministry began with Israel, as God had promised. After the resurrection he sent his disciples to all nations (Matthew 28:19); this woman was an early sign of that.