In the Bible there are several stories which are embarrassing to the character involved. I like that the Bible has kept these potentially embarrassing stories in the scripture because it lends it an air of authenticity. It is the stories told of people who are obviously not perfect still being used by God which gives us the sense that these stories are not only true, but that we could be used by God for good despite ourselves.
Jesus is the exception. Jesus, being the very word of God made flesh, who nature and character is that of God, is in a different category. So, when Jesus seems to step out of the character of wise, kind, and caring to all people – it is uncomfortable.
The woman came and knelt before him. “Lord, help me!” she said. He replied, “It is not right to take the children’s bread and toss it to their dogs.” “Yes, Lord,” she said, “but even the dogs eat the crumbs that fall from their masters’ table.”