Regarding calling gentiles dogs: To quote from Life Application Study Bible in reference to Matthew 15:24:
Jesus' words do not contradict the truth that God's message is for all people. After all, when Jesus said these words, He was in Gentile territory on a mission to Gentile people. He ministered to Gentiles on many other occasions also. Jesus was simply telling the woman that Jews were to have the first opportunity to accept Him as the Messiah because God wanted them to present the message of salvation to the rest of the world. Jesus was not rejecting the Gentile woman. He may have wanted to test her faith, or He may have wanted to use the situation as another opportunity to teach that faith is available to all people. Had she taken what He said as an insult, as it may sound to us today, her faith would have been damaged and her daughter would not have been healed. It is obvious that she understood His reference as nothing more than a metaphor. Much the same as we are referred to as sheep.
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