For whom did Jesus come? (Matthew 15; Mark 7)

In both Matthew 15 and Mark 7 readers are confronted by a very unusual story: a foreign woman begs Jesus to cast a demon out of her daughter.  It seems like Jesus would honor the request as He did for countless others, but He instead speaks harsh words to her about not taking the children's bread and feeding it to the dogs.  If you've read many of Jesus' words, then you recognize that this was a very atypical response.  Some suggest that Jesus was quoting a popular proverb and therefore wouldn't have come across in very negative manner.  Other commentators suggest that Jesus was testing her to see how much faith she truly had.  Apparently the woman had a great amount of faith because her persistence led to the exorcism of the demon and revealed that Jesus' mission was two-fold: first to rescue the Israelites, and then to rescue the Gentiles – a focus that wouldn't exist until after His death.  The truth is that Jesus came for all people – Hebrew, Greek, Roman, and Gentile – with the desire that all should find a restored relationship with the Heavenly Father.