A Puritan Answer
This answer is an attempt at an exposition of a comment that Richard Sibbes makes in his book Josiah's Reformation:
God doth always hear, though he seemeth not to hear sometimes, to increase our importunity. Christ heard the woman of Canaan at first; but yet, to increase her importunity, he gave her the repulse and denial, and with the same, inward strength to wrestle with him. (123)
This passage is a marvelous example of the interplay that, without relinquishing one bit of his sovereignty for even a moment, God with loving condescension chooses to have with his creatures. Christ here teaches us about the way he relates to us, and about prayer.
Prayer and Intercession as Struggle in the Bible
The Scriptures are full of examples of people who struggled with God in (often intercessory) prayer:
- Abraham pressed God hard when he interceded for Sodom.
- Isaac cried out for maybe twenty years over the barrenness of Rebekah.
- Jacob wrestled with God all night long. Even when injured, he refused to let go until he received the blessing he sought.
- On multiple occasions, Moses boldly argues with God about his announced plans to destroy the people of Israel, and prevails.
- Hannah prayed so passionately she made a devout and godly priest, a man not unacquainted with prayer, think that she was drunk. Her prayers spanned a number of years before being answered.
- David intensely mourned Bathsheba's child while the child lived, even though God had decreed to kill the child. Though God did not answer his prayer, neither was David condemned for his actions.
- In the transference of the office of prophet from Elijah to Elisha, Elisha refuses to listen to Elijah's repeated exhortations to stay behind, even though Elijah was a great prophet and spoke for God. But pressing on was what God actually wanted him to do, and the struggle served as a test and preparation for his own prophetic ministry.
- Other Old Testament examples could be named; Daniel, Nehemiah and Ezra were all men of fervent, prolonged prayer.
- Jesus' own parables of the importunate widow and the knocking neighbor.
- Paul uses "struggle" as a term for prayer, both with reference to himself and Epaphras. The nature of this prayer seems to be prominently intercessory.
Interplay in the Role and the Person of Jesus
In Christ, we are all able to struggle with God. Jesus himself, though, as our mediator is the primary one who gives importunate, intercessory prayer. In his sleepless strength, he prays passionately for us beyond any passion we have ever felt, day and night, with wisdom and knowledge we shall never even approach. Christ is the one who struggles with God in this type of prayer; I cite the entire book of Hebrews on this point.
I find this profoundly baffling. Surely, those who paint God the Father as the angry person of the Trinity and Jesus as the loving person blaspheme the Most High. However, if we step too far in the other direction, we deny the need for an atonement sacrifice and a high priest. Jesus is truly the mediator with the Father. Once again, an immutable God, who has loved his own from eternity, reveals himself to us in mutable concepts, that is, that he needs to be passified by the continual intercession of Christ for us to be acceptable to him.
Jesus as God-man is supremely able to have interaction with his creatures and to be affected by them (yet somehow without ceasing to be supreme ruler). We see that in Mark's telling of this very story:
He didn't want anyone to know which house he was staying in, but he couldn’t keep it a secret. —Mark 7:24 (NLT)
His mourning for Lazarus also comes to mind.
Conclusion
Jesus' interaction with the Syrophoencian woman, like many similar cases in Scripture, shows that he cares to be more to us than a database which can be queried for results, and more to us than an impersonal deity who mechanistically orders the universe. He graciously summons us to struggle with him, so that we might avoid apathy and fatalism. Prayer is a means of grace; he would not have us malnourished.
It delights him when someone pursues him so wholeheartedly that when even he himself throws impediments in the way, the pursuit continues. He is too kind to let us be lukewarm.
Sibbes continues his discussion by saying,
God seems not to hear, because he delights in the music of his children's prayers. Oh how he loves to hear the voice of his children! As a Father to hear the language of his child, though it be none of the best; so it is sweet music in God's ear to hear the prayer of his children. He will have prayers to be cries. Therefore he defers to hear; but in deferring he doth not defer, for he increaseth our strength, as Jacob's wrestling, that we might cry after him, wrestle with him, and offer violence unto him again.