“I was sent only to the lost sheep of the house of Israel.” At first glance, Jesus’ statement concerning the healing of the Syrophoenician woman’s daughter seems hard, cold, and difficult to understand, but we must understand it in the context of his earthly mission and what God sent him to do.
The Greek word translated “sent” is the common Greek word apostellō (#649 ἀποστέλλω), from which we get the English word “apostle,” meaning, “one who is sent.” Apostellō often simply means “to send away, dismiss, allow one to depart.” However, it often has the meaning listed first in the BDAG Greek-English lexicon, which is “to dispatch someone for the achievement of some objective,” and that is the meaning it has here in Matthew 15:24. That is why R. C. H. Lenski translated the word as “commissioned,” that Jesus was only commissioned to go to the lost sheep of Israel (Lenski, The Interpretation of St. Matthew’s Gospel). Jesus was commissioned by God to go to the lost sheep of Israel; that was the specific mission God sent him on, and although that mission involved being the sin-offering for the sins of the world (cp. 2 Cor. 5:21), in his earthly ministry he was specifically to go to Israel and call it back to God.
We see evidence of Jesus’ specific mission to Israel in the fact that, earlier, when he sent his disciples out to evangelize, he told them to go only to Israelite towns. He said, “Do not go on any road of the Gentiles, and do not enter into any city of the Samaritans, but go instead to the lost sheep of the house of Israel” (Matt. 10:5-6). It is not that Jesus did not care about the Gentiles, but rather that at that time in history his specific ministry was to the Jews. That had to do with the Jews being God’s chosen people and the covenant that God made with Israel (Exod. 24:3-8). God loves the world (John 3:16) but He redeemed the world through Jesus Christ, who was a Jew and was specifically sent to the Jews first. Later he would command his disciples to evangelize the whole world (Matt. 28:19; Acts 1:8).
Although Jesus’ specific mission while he was on earth was to Israel and set the stage for the fulfillment of prophecies such as Isaiah 61:3, he also fulfilled the prophecies such as the ones in Isaiah 42:6 and 49:6 that he was to be a light to the Gentiles. We see that in the fact that Jesus did occasionally minister to Gentiles or in Gentile areas. For example, he healed people from Syria, which was a Gentile area (Matt. 4:24), a Roman soldier’s servant (Matt. 8:5-13), men afflicted by demons (Matt. 8:28-34); and a Samaritan woman (John 4:1-42). Also, after going to the region of Tyre and Sidon where he healed the woman’s demon-possessed daughter, he went into the Decapolis, a Gentile area, and healed a man who was deaf and dumb (Mark 7:31-37) and many others as well (Matt. 15:30), and he also fed the 4,000 in the same area (Matt. 15:29-39, Mark 8:1-9). But although Jesus did heal Gentiles as we see here in Matthew 15:21-28, he said what is recorded here in Matthew 15:24 to teach and remind his followers that his earthly ministry was to Israel.
However, Jesus certainly knew that his ministry would one day lead to his conquest of the whole earth and reigning over the whole earth as king, so, for example, in John 10:16 he spoke of the future when all believers would be one flock with one “shepherd” (king: the word “shepherd” was often used idiomatically for “king,” see commentary on Jer. 2:8). That is why he told his followers that he had other sheep (Gentiles) that were not of “this fold” (Israel), and that he must bring them to himself also (John 10:16), and why, after his resurrection, he told his disciples to tell the whole world about him.