21 Then Jesus went out from there and departed to the region of Tyre and Sidon.
22 And behold, a woman of Canaan came from that region and cried out to Him, saying, “Have mercy on me, O Lord, Son of David! My daughter is severely demon-possessed.”
23 But He answered her not a word. And His disciples came and urged Him, saying, “Send her away, for she cries out after us.”
24 But He answered and said, “I was not sent except to the lost sheep of the house of Israel.”
25 Then she came and worshiped Him, saying, “Lord, help me!”
26 But He answered and said, “It is not good to take the children’s bread and throw it to the little dogs.”
27 And she said, “Yes, Lord, yet even the little dogs eat the crumbs which fall from their masters’ table.”
28 Then Jesus answered and said to her, “O woman, great is your faith! Let it be to you as you desire.” And her daughter was healed from that very hour.
Tyre and Sidon (v.21) — Along the coast northwest of the Sea of Galilee — outside Herod’s jurisdiction. This is the only recorded instance during His ministry when the Lord left Palastine.
woman of Canaan (v.22) — Mark (7:26) says she was Greek (meaning Gentile), a Syro-Phoenician by birth.
send her away (v.23) — Based on the way Jesus responds (in v.24), it is probable that the disciples were urging Him to give her what she wanted so she would go away.
dogs (v.26) = little dogs, pets
Most of my commentaries explain this passage with some ideas that make sense to me, but none of them paint the whole picture, so I’ll summarized in my own words.
Jesus came as the Messiah of Israel. His ministry was only to the Jews. When this Gentile woman approached Him as the Son of David, she had no claim on Him. She was one of those who were … without Christ, being aliens from the commonwealth of Israel and strangers from the covenants of promise, having no hope and without God in the world (Ephesians 2:12). On this basis, He said nothing.
When the disciples asked Him (probably) to give her what she wanted so they could be rid of her, He explained, “I was not sent except to the lost sheep of the house of Israel” (v.24).
She asked Him again to help her daughter, this time dropping her claim. He again explained the higher position of Israel, “It is not good to take the children’s bread and throw it to the little dogs” (v.26).
She then asked a third time, and this time she worded her request in such a way that Jesus could grant her request. “Yes, Lord, yet even the little dogs eat the crumbs which fall from their masters’ table.”
The word “masters'” is plural. She wasn’t referring to Him as her master but to those who were fed at the table — the Jews. She had come to the understanding that her blessing could only come through Israel.
This is where my commentaries miss the point, in my opinion. This experience wasn’t given to us to show that salvation was about to be taken from Israel and given to the Gentiles. The Lord was still teaching the kingdom message. A major point of that kingdom message is that the nations will be blessed through Israel. This passage underlines that point exactly.