Nelson happenings

About two or three times a year I'll have a question in Sunday School that nobody seems to be able to answer, or I get an answer I feel is a blow-off. Today was one of those days, and I thought I'd pose the question here. This could be a lengthy blog post. The lesson started by discussing Matthew 15:22-28, which is about a Canaanite woman who wants Christ to heal her daughter. Christ has what appears to be some harsh words for her. I don't understand why. The initial answer was that Christ was sent to minister to the Jews, not the Gentiles. Yes, that's true, but wouldn't it be just as easy as to help her the first time? To me, comparing her to a house dog is insulting. And while it may have been the Jewish culture to refer to gentiles as dogs, I would have expected Christ to not follow that. I also pointed out that in John 4, Christ goes to a Samaritan woman and teaches her. So why did he not help the woman in Matthew initially? The answer I got to this is that Christ was probably distracted, preparing for the mount of Transfiguration. That was the end of that discussion, and it doesn't gel with me. I've done a little research and can't find a satisfactory answer. So, I pose the question to all of you. I understand that it was necessary to test her faith, but why compare her to a dog?