Matthew 15:22-28
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.
But he answered her not a word. And his disciples came and besought him, saying, Send her away; for she crieth after us.
But he answered and said, I am not sent but unto the lost sheep of the house of Israel.
Then came she and worshipped him, saying, Lord, help me.
But he answered and said, It is not right to take the children's bread, and to cast it to dogs.
And she said, Truth, Lord: yet the dogs eat of the crumbs which fall from their masters' table.
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 Gentile woman and her family had no covenant with God and no right to approach Christ.
Only Israel had a covenant (and high priest) with God.
Those cut off from God are dogs, and Jesus rightfully called the woman a dog.
Revelation 22:14-15
Blessed are they that do his commandments, that they may have right to the tree of life, and may enter in through the gates into the city.
For without are dogs, and sorcerers, and whoremongers, and murderers, and idolaters, and whosoever loveth and maketh a lie.
Philippians 3:2
Beware of dogs, beware of evil workers, beware of the concision.
Deuteronomy 23:18
Thou shalt not bring the hire of a whore, or the price of a dog, into the house of the LORD thy God for any vow: for even both these are abomination unto the LORD thy God.
Her response was one of the most humble and faithful moments in the Bible:
It’s true Lord, I am a dog; I have no right to the children’s bread. But all I need are crumbs to heal my daughter. Just a crumb of the Lord will do.
Foreshadowing the New Covenant, Christ welcomed her.
But she had first to admit and accept who she was: a dog.