In Matthew 15:21–28, Jesus encounters a Canaanite (Syrophoenician) woman who begs Him to cure her daughter. Jesus initially refuses her request by saying, “It is not right to take the children’s bread and toss it to the dogs” (Matthew 15:26). Taken out of context, and especially in English, it’s easy to mistake this for an insult. In the flow of the story, however, it’s clear Jesus is creating a metaphor meant to explain the priorities of His ministry. He is also teaching an important lesson to His disciples.
Jews in Jesus’ day sometimes referred to Gentiles as “dogs.” In Greek, this word is kuon, meaning “wild cur” (Matthew 7:6; Luke 16:21; Philippians 3:2). Non-Jews were considered so unspiritual that even being in their presence could make a person ceremonially unclean (John 18:28). Much of Jesus’ ministry, however, involved turning expectations and prejudices on their heads (Matthew 11:19; John 4:9–10). According to Matthew’s narrative, Jesus left Israel and went into Tyre and Sidon, which was Gentile territory (Matthew 15:21). When the Canaanite woman approached and repeatedly asked for healing, the disciples were annoyed and asked Jesus to send her away (Matthew 15:23).
At this point, Jesus explained His current ministry in a way that both the woman and the watching disciples could understand. At that time, His duty was to the people of Israel, not to the Gentiles (Matthew 15:24). Recklessly taking His attention from Israel, in violation of His mission, would be like a father taking food from his children in order to throw it to their pets (Matthews 15:26). The exact word Jesus used here, in Greek, was kunarion, meaning “small dog” or “pet dog.” This is a completely different word from the term kuon, used to refer to unspiritual people or to an “unclean” animal.
Jesus frequently tested people to prove their intentions, often through response questions or challenges (see John 4:16–18; and 4:50–53). His response to the Canaanite woman is similar. In testing her, Jesus declined her request and explained that she had no legitimate expectation of His help. The woman, however, lived out the principle Jesus Himself taught in the parable of the persistent widow (Luke 18:1–8). Her response proved that she understood fully what Jesus was saying, yet had enough conviction to ask anyway (Matthew 15:27). Jesus acknowledged her faith—calling it “great”—and granted her request (Matthew 15:28).
So, according to both the context and language involved, Jesus wasn’t referring to the Canaanite woman as a “dog,” either directly or indirectly. He wasn’t using an epithet or racial slur but making a point about the priorities He’d been given by God. He was also testing the faith of the woman and teaching an important lesson to His disciples.
source: gotquestions.org