The way I understand this has to do a bit with God's corporate election of people. At the time Jesus was on this earth, the Israelites where still God's chosen people (and still are, just have been set aside for the time being) to achieve his purposes. As such, Jesus came to preach and teach to Jews (the children who get the bread), not Gentiles (the dogs under the table). The woman in this passage was a gentile.
In v27, Jesus was telling her that he came for the benefit of the Jews at that specific moment, not the gentiles. Which is true, because at that point in time, the world had not yet entered the church age (the time we're living in now) in which God uses gentiles to fulfill his purposes. So, in this verse he wasn't dismissing her, he was using this little exercise with her as a test of her faith.
Her answer in v28 proved to Jesus (not that he really needed proof, but it shows a response from the person, as is required of us in order to be saved) that she knew who he was and was placing her faith in him. To explain it another way, when she said "but even the dogs under the table eat the children's crumbs", she was humbling herself before God, (she acknowledged her position in relation to Jesus and the Jews), and she was placing complete faith in Jesus (she acknowledged that Jesus was the source of the "bread" by calling him Lord and without him she was helpless).
Had this woman not had the kind of faith in Jesus that God requires, her response to Jesus statement would probably have been one of despair and self-pity. A lot of times when we don't get what we pray for, don't we typically respond to God with anger, resentment, despair, self-pity, or other similar negative feelings? But her response wasn't like that, it was one of complete faith and trust in Jesus.
v29 is Jesus response to her faith in him. Because she humbled herself before God and put her complete trust in him, her request was granted.
She is an example of the kind of faith that we all should have as Christians.
I hope that helps shed some light on this passage for you.
Last edited by fracturedInfinity; September 24th, 2008 at 10:23 AM.
"I do not seek to understand that I may believe, but I believe that I may understand: for this I also believe, that unless I believe I will not understand." --Anselm of Canterbury
For consider Him who endured such hostility from sinners against Himself, lest you become weary and discouraged in your souls. You have not yet resisted to bloodshed, striving against sin.