What does Matthew 15:28 mean?
Jesus initially resisted healing a Canaanite woman's daughter. At least, He has given the appearance of resisting. He has told her His mission is only to the lost sheep of Israel. In a statement easily misunderstood, He told her that children's bread should not be given to dogs (Matthew 15:21–26).The woman persisted as only the parent of a sick child can. She has knelt and pleaded. She has refused to take offense at an analogy that pictures her people as dogs. Instead of focusing on what symbols were used, she fully understood the point being made. Christ is not insulting her, or her people, but pointing out that He has an obligation to offer His "bread" to the children of God.
In response—showing both great wisdom and great humility—she answered that the Master, Jesus, can choose to allow the dogs to eat the crumbs. In other words, that which was offered to "the children," and either wasted or rejected, is something the master would happily let others take. In all this, she has never wavered in being convinced that Jesus is truly the Messiah and that it is within His power to cast the demon from her daughter.
Apparently in delight, Jesus praises the greatness of her faith and says it will be done for her as she desires. His intent was never to deny her a miracle, but to demonstrate and illustrate her faith.
Instantly, her daughter is healed. The term used implies the demon had caused the girl to be sick or afflicted in some way. With the demon gone, the affliction is gone, as well.