"And she said, Truth, Lord: yet the dogs eat of the crumbs which fall from their masters’ table."
You have to read the full story to remember how difficult this passage is to read today, when we know that being born a Canaanite (or any other -ite) should not be a big deal, and certainly doesn't make one person any less worthy than another. And yet that seems to be exactly what's going on in this story. And as faith-filled and clever as the woman's response is, it can still be hard for us today to feel good about a woman referring to herself as a dog.
A few possible explanations:
-In Mark's telling of what is presumably the same story, Jesus is trying to keep a low profile so that he can get where he's going without a multitude following him when this woman comes loudly begging for help (see Mark 7: 24-25). In that reading, Jesus' reluctance probably has more to do with procedure than ethnicity: here's someone being rebuked for asking in the wrong way at the wrong time, which we modern readers much prefer to someone being rebuked for being of the wrong race.
-I've heard, though never confirmed, that the word Jesus uses for "dog" is one that referred to a domesticated house pet, as opposed to the highly unpopular wild dogs who roamed the streets. If that's the case, Jesus' rebuke is at least gentler, and possibly even intended to help elicit her response, showing the shocked disciples why she is worthy of the Lord's time and attention.
-D&C 93: 12 reports that Jesus, though sinless, did evolve, learn, and grow. We could read this passage as one in which Jesus is righteously focused on his mission as he understands it, but then is taught by this encounter something profound about the breadth of his own mortal mission.
-John 9: 3 says that sometimes hard-to-understand things happen simply so that God will have a place to show us something good and important. Maybe the whole exchange happens so that we can have, written in our scriptures, an image that says that even the most marginalized people (she is after all, a Canaanite, less respected than Gentile or Samaritan) are inexorably connected with us. That we are as totally connected to and responsible for the "dog" as for "the children." (Imagine an Israel today in which the access of the average Palestinian worker to the "crumbs" of the Israeli economy played as great a role in policy formation as security concerns. I'm not naive enough as to believe any change in policy could solve that region's problems, but that shift in thinking could probably do a lot to ease the pain of certain innocent bystanders.) Maybe Christ is working within the power relationships of his time not because he believes in them, but because talking within them will show something valuable to us.
In any case, there are some thoughts on this passage, although all this talk of connection has me thinking again of the banyan tree...