Was the Canaanite woman demanding the Jesus exorcise the demon and save her daughter? Some of the translations make it sound like she was.
She is pleading with Jesus, who eventually says, “I was sent only to the lost sheep of Israel” (v 24). She replies, “Lord, help me!” (v 25). (Greek students: you should memorize her answer for the next time you need help in Greek class — κύριε, βοήθει μοι.) Jesus responds, “It is not right to take the children’s bread and toss it to the dogs” (v 26).
If you don’t know the story, it would look like Jesus was truly cruel, but I am sure he was pressing her to exercise her faith, if for no other reason to show the disciples what true faith looked like. She truly believed Jesus could save her daughter.
The NIV translates her answer, “‘Yes it is (ναί), Lord,’ she said. ‘Even (καὶ γὰρ) the dogs eat the crumbs that fall from their master’s table’” (v 27). Doesn’t that sound like she is saying, “Yes, it is right to take the children’s bread and give it to the dogs.”
However, she is really agreeing with Jesus’ statement that it is not right to do so. ναί is a “particle denoting affirmation, agreement, or emphasis,” “certainly, indeed, quite so” (BDAG).