Jesus response to a desperate woman with a demon-possessed child seems so mean, “First let the children eat all they want,” he told her, “for it is not right to take the children’s bread and toss it to the dogs.” (Mark 7:27)
He didn't just refuse her. He called her a dog! That’s not the response she (or we) expected. The woman was not Jewish. The Jews considered all Gentiles (non-Jews) to be unclean, contaminated by paganism and impurity. Jesus' response is as much for the audience of supporters and enemies as it is for the woman. He is saying that he should finish his ministry in Israel before branching out.
Paul would later write, "I am not ashamed of the good news because it is the power of God for the salvation of everyone who believers: first for the Jew and then for the Gentile." (Romans 1:16)
The woman's rebuttal is amazing. She uses Jesus imagery to make her case saying that even dogs eat the crumbs that fall from the children’s table. She needed a miracle for her child that only Jesus could provide. She did not need much, merely a crumb.
This woman shows insight into the teachings of Jesus that his closest followers lacked. Her response is both humble and bold at the same time.
Jesus was impressed with her undivided heart, her persistent faith, and her willingness to settle for crumbs. He says, “For such a reply, you may go; the demon has left your daughter.” (Mark 7:29)
Through this gesture, Jesus tells us that everybody is welcome to God's party. He is reminding us that God called Abraham to be a blessing for all nations. No matter who you are or where you come from, you are welcome to the party.