The Faith of the Canaanite Woman
21 Then Jesus went thence, and departed into the coasts of Tyre and Sidon. 22 And, behold, a woman of Canaan came out of the same coasts, and cried unto him, saying, Have mercy on me, O Lord, thou Son of David; my daughter is grievously vexed with a devil. 23 But he answered her not a word. And his disciples came and besought him, saying, Send her away; for she crieth after us. 24 But he answered and said, I am not sent but unto the lost sheep of the house of Israel. 25 Then came she and worshipped him, saying, Lord, help me. 26 But he answered and said, It is not meet to take the children’s bread, and to cast it to dogs. 27 And she said, Truth, Lord: yet the dogs eat of the crumbs which fall from their masters’ table. 28 Then Jesus answered and said unto her, O woman, great is thy faith: be it unto thee even as thou wilt. And her daughter was made whole from that very hour.
The woman was a pagan who was living outside the blessings of the Mosaic covenant. She was shut out from the blessings of a covenant relationship with God. She was reduced to scavenging for a few scraps or crumbs to satisfy her spiritual hunger just like the dogs in the parable. This is a likeness to the way of life of a dog. It was forced on her by circumstances and not a natural trait of her being.
Jesus was not impugning her moral character or making her out to be something less than human or a lower form of humanity. The Koran actually does this in reference to the Jews calling them pigs and apes. They are still called this all over the islamic world.