What does Matthew 15:26 mean?

To avoid crowds and religious leaders for a while, Jesus is in the Gentile district of Tyre and Sidon. He is likely exhausted at this point in His ministry (Matthew 13:1–2; 14:13–14, 34–36).

Somehow, a believing Canaanite woman has found Him here. She is not Jewish, but she likely believes He is the Messiah and that He can cast a demon from her daughter (Matthew 15:21–23). Jesus has refused because His designated mission—for now—is only to Israelites (Matthew 15:26). What Jesus says in this verse is often torn from that context, and the words which follow, to make it seem derogatory, or even hateful. It's neither: Jesus has a purpose for this dialogue (Matthew 15:28).

However, these words would have been difficult for the woman to hear, regardless. Christ's intent, apparently, is to test the woman's commitment to her request, and her faith in Him. Jewish people sometimes called Gentiles "dogs" to show their disrespect for them. Dogs in the ancient middle east were most often seen running in packs, as dangerous scavengers. Jewish people would not, in general, think of them as either pets or friendly creatures.

However, the word Jesus uses is not as harsh as it sounds when translated into English. The Greek term He uses, kynariois, literally means "little dog." In the context of children and food, this seems to be a reference to a pet; this would have been a more common use of dogs in a Gentile region.

There's no question that Jesus' symbolism here depicts Israelites as God's children and this woman—or her child—as a "little dog;" not even as a person. However, Jesus is not trying to be hurtful. He is comparing the nature of God's relationship with His chosen people Israel to those in the rest of the world who practice pagan idolatry. He says this to prove the woman's humility and faith, knowing He will shortly reward both (Matthew 15:28).