Was Jesus Racist?

Matthew 15:21-28

This is an odd encounter. First, Jesus does not respond at all to the pleas of this Canaanite woman and then, at his disciples' urging, he tries to send her away. He even compares her and her people to dogs. This doesn't seem like the Jesus we know and love. This doesn't seem like the Jesus we like to portray. In the end he heals the woman's daughter and commends her faith but he certainly made her work pretty hard to get there and seemed to feed, or at least reflect, the racist attitudes of the day in the process.
Perhaps Jesus was holding a mirror up for his disciples and the rest of Jewish society to see. Perhaps he was trying to get them to realize how abhorrent their attitude toward the outsider was. I'd like to think that's what Jesus was doing but I don't see him driving that point home through any kind of teaching coming out of this encounter.
It also raises the question of why Matthew would include this story in his book. I think it's probably to show that Jesus was not just the King of the Jews but that his message of the kingdom was going to spread to people of all races and nations.
Personally, this story makes me evaluate my own attitude toward the outsider. I certainly hold some prejudices about certain races and classes of people. I wonder what I would see if Jesus were to reflect back to me my own prejudices. This has been my prayer for a long time: Lord, help me to see people through your eyes and to love them with your love.