In Matthew 15 21:28 Jesus shows some bigotry towards a Canaanite woman by referring to her as a dog. Was Jesus wrong and the woman right, why did Jesus change his mind and do as she asked?
Jesus was right and didn’t change his mind. Jesus said: "I wasn't sent to anyone but the lost sheep of the house of Israel.". And that is true, he was sent for Jews. Reason who Jesus did what was asked is that the woman showed faith ("Woman, great is your faith! Be it done to you even as you desire.").