Matthew Chapter 15

Mt.15:26 But He answered and said, “It is not good to take the children’s bread and throw it to the little dogs.”
Mt.15:27 And she said, “Yes, Lord, yet even the little dogs eat the crumbs which fall from their masters’ table.”

Actually the woman of Canaan was a very intelligent and clever. If Jesus would have said this to me, the only thing I would do is to continue shouting and crying or just to give it up and leave. But she did not just continued crying but told him a reason, why her daughter also has the chance/right (not really a right.. more like an opportunity) to be healed. This strong faith and will impressed Jesus. So Jesus granted her, what she wanted.