In Matthew 7:6 Jesus calls unbelievers dogs and swine, and in Matthew 15:26 Jesus likens both the Canaanite woman and Gentiles to dogs.
Jesus was using common Jewish metaphors to illustrate an unbeliever’s or pagan’s total depravity.
Read Proverbs 26:1; 2 Peter 2:22; & Rev. 22:14
The crowds would have understood that Jesus was obviously using metaphorical language, and was not literally calling someone a dog or swine.
In regards to Jesus’ statement in Matthew 15:26, Christ was trying to illustrate a key point to his disciples.
According to first century Jewish thought both Gentiles and women were held in low esteem.
Jews regarded themselves as the children of God, whereas Gentiles were nothing more than house pets.
The Greek word used in this verse for dogs is kynarion, which properly translated means house pet or puppy [verification: Strong’s #2952].
Jesus’ use of this term implies that just as a house pet has a place in the home of his master, so too do the Gentiles have a place prepared for them in God’s kingdom.
Christ was trying to move his Jewish disciples, who had tried earlier to get rid of the Canaanite woman, to envy by the woman’s persistence and display of great faith; a faith exemplified by someone who to them was nothing more than a house pet.
In similar fashion, Jesus had used a Roman Centurion’s faith in contrast to the Israelites’ lack of faith:
"Now when Jesus heard this, he marveled, and said to those who were following, `Truly I say to you, I have not found such great faith with anyone in Israel. And I say to you, that many shall come from East and West, and recline at the table with Abraham, and Isaac, and Jacob in the kingdom of heaven; but the sons of the Kingdom shall be cast out into the outer darkness; in that place there shall be weeping and gnashing of teeth.’ " Matthew 8:5-12
The Jews considered Romans as enemies which God would destroy when Messiah would appear.
And yet here was Israel’s Messiah commending the faith of such a one.
Hence, Jesus was using Gentiles as examples for Israel to emulate, not look down upon.