Our false image of God can get in the way of completely receiving his mercy. When that happens often desperately grasp after other things in order to try and earn our way to heaven. This grasping, which is sin, harms us and harms others. It will cause us to lose the joy that we should have as Christians.
For her benefit and for our benefit, the Lord draws faith out of the Canaanite woman. She becomes a remarkable example of what trusting prayer in faith looks like. For when we desire in prayer, nothing other than the will of God, then it will be done in our lives.
If we admit our need before God, our weaknesses are not the end of the story but only its beginning.