For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Richard Hunt
As Jesus was beginning His ministry, His focus was on the people of Israel. In context, the woman asking for help from Jesus was a Gentile. The "children" were Israel. The "dogs" are all Gentiles. He used this encounter to show His mission to offer God's salvation not only to the "children" but also the "dogs" who have faith and believe.
If you have faith to believe Jesus died to pay for your sins, and that He rose from the grave to defeat death and give eternal life in heaven, you can receive this wonderful gift.
john kishpaugh
I borrow some from Bishop Barron (Word on Fire). "The story of the conversation with the Syrophoenician woman is one of those famously problematic passages in the old testament." BB. She say and I add my interpretation/clarification: "Sir, even the dogs ( gentiles ) under the table (near Israel) eat the children's ( Jews ) crumbs" Meaning the gentiles benefit from Gods blessings for the Jewish people, thus showing faith. "At this point, Jesus praises her for her faith and cures her daughter" BB. The strength of her faith shows itself" BB
Jack Gutknecht
I borrow a hymn from Edward Henry Bickersteth.
Not Worthy, Lord, To Gather Up The Crumbs
"Not worthy, Lord, to gather up the crumbs
With trembling hand that from Thy table fall,
A weary, heavy laden sinner comes
To plead Thy promise and obey Thy call.
I am not worthy to be thought Thy child,
Nor sit the last and lowest at Thy board;
Too long a wanderer and too oft beguiled;
I only ask one reconciling word.
One word from Thee, my Lord, one smile, one look,
And I could face the cold, rough world again;
And with that treasure in my heart could brook
The wrath of devils and the scorn of men.
And is not mercy Thy prerogative—
Free mercy, boundless, fathomless, divine?
Me, Lord, the chief of sinners, me forgive,
And Thine the greater glory, only Thine.
I hear Thy voice; Thou bidd’st me come and rest;
I come, I kneel, I clasp Thy piercèd feet;
Thou bidd’st me take my place, a welcome guest
Among Thy saints, and of Thy banquet eat.
My praise can only breathe itself in prayer,
My prayer can only lose itself in Thee;
Dwell Thou forever in my heart, and there,
Lord, let me sup with Thee; sup Thou with me."
Daniel Veler
The bread was the same principle used with the parable of the pearls. Cast not you pearls before the swine.
Matthew 7: 6: Give not that which is holy unto the dogs, neither cast ye your pearls before swine, lest they trample them under their feet, and turn again and rend you.