This past Wednesday our adult Bible study looked at Mark 7.14-30. Verses 14-23 expound upon verses 1-13, in which Jesus declares that man-centered traditions have no bearing on the commandment of God, and usually serve to muddy the waters when it comes to actually obeying what God has said to do. He then goes on to declare that "There is nothing outside a person that by going into him can defile, but the things that come out of a person are what defile him." This principle is illustrated by verses 24-30 when he has an encounter with a gentile woman and heals her daughter of a demon possession.
If the latter is what Jesus was intending, then he was using what was akin to a racial slur, as dogs were lowly, bothersome pests in first century Jewish culture. They certainly were not the domesticated animals that we enjoy today. To refer to someone as a dog would have been highly offensive.
A second option for interpretation of this phrase is that Jesus is referring to an order in his ministry - that he came, first, to seek and to save that which was lost (the children of Israel) and that his primary ministry is to them, and to gentiles secondarily. This, to me, is the preferred and more likely interpretation.
Unfortunately there are many Christians who have entertained the notion of Jesus using racial slurs (and therefore sinning by being a racist) in perceived attempts to accentuate his humanity, presuming that Jesus was so human that he was even caught up in cultural racial snares. Surprisingly, they don't realize the drastic effects this has on the rest of their theology, and how it essentially negates the sufficiency of his atonement. Put simply, if Jesus was a racist (a sinner) then his sacrifice was not sufficient, nor was his righteousness pure. Put even more simply, if Jesus was a racist, he can't be the Messiah nor the Son of God. (For an unfortunate analysis that affirms an interpretation identifying Jesus as a racist in this situation, see this treatment of this text)
But there are, I think, good reasons to not interpret Jesus' statement as a racial slur but instead a statement of the order of his ministry. Those reasons are as follows:
1. It is clear throughout scripture that Jesus has come first and foremost for the Jews. Indeed, his appearance on the scene at all was in fulfillment of a promise to Abraham and the Jewish nation - that Jesus would bless Israel, and the world, through her (see Genesis 12). And when Jesus says that he has come to seek and to save that which was lost, he is referring to the nation of Israel (see Luke 19). Furthermore, Jesus speaks about Israel as his sheep, and as himself as their shepherd (see John 10). The examples go on and on. Put simply, it is clear from both testaments that the primary ministry of the Messiah was to reconcile God's people to himself. And it is also clear that gentiles were a secondary concern in his earthly ministry. This fact is easily observed throughout the gospels. The rest of the context of the narrative between Jesus and this woman exposes this - and the woman gets it. In fact, it's her grasp of this reality that exposes her faith in him. What Jesus means by this expression is that his primary purpose is to feed his children (Israelites). His secondary purpose will be to feed others. (In the example he used, this would refer to "dogs." Note: there is some question as to the Greek word translated "dogs," in that it might be better translated "puppies." If nothing else, this should lessen the effect of the use of the word for those who think that Jesus was using a racial epithet.)
2. The notion that Jesus would be prejudiced against gentiles flies in the face of his actual interaction with gentiles in the gospels - including his treatment of the Syrophoenician woman. In other words, it is clearly observable that Jesus was not prejudiced against gentiles because his interaction with them says differently. If he didn't like them, then why did he go to such great lengths to serve and minister to them? The testimony of Jesus' interaction with gentiles adequately argues against the perception that he was prejudiced against them.
3. Finally, as I've already alluded to, if Jesus was a racist, then Christian theology and the message of the gospel is doomed and is not salvific. In other words, if Jesus sinned by being a racist, then I have no hope of salvation through his life and death. He cannot give me his righteousness, because it is stained with sin. He cannot pay my sin debt, because he would have to pay for his own. If Jesus is a racist, the gospel goes away. But this notion is so unbiblical (and by "unbiblical" I mean that it flies in the face of the rest of the Bible) as to be absurd. If anyone thinks that Jesus has sinned, then they haven't read the rest of the Bible or even the rest of the gospels.
So no, Jesus was not a racist, and he didn't use a racial slur against the Syrophoenician woman. There is a mountain of evidence (and common sense) to support that.