According to John Owen, parents will feel a "natural affection," (i.e., an affection that is part of their nature according to God's creative act) toward their children and work to provide for them. Owen notes that this is not unique to human beings, but they share this inner purpose with the other creatures that bear children. Elephants, frogs, clown fish (I'm looking at you Nemo), and humans all share this instinctual concern for their offspring. It is what he calls the parental "law of operation," or what we might think of as the intrinsic purpose of parenthood. Yet, human parents do have one major difference from their animalian counterparts—they are created in the image of God and are responsible to Him for their actions. Consequently, they are not merely to provide for their children as an instinctual impulse, but as a humble act of submission and obedience to the God who created them.
This turns out to be quite a problem. Since human parents are as "naturally" opposed to the rule of God in their lives as they are "naturally" inclined to care for their children, there are bound to be conflicts. We see it on the news all the time: parents murder their children, mistreat them, neglect them. Even non-Christians are repulsed at these things, it's unnatural! Sin's power is so strong in the unregenerate person that it can overrun something as deeply ingrained as the parent's instinctual impulse to care for his or her children. Owen puts a fine point on it when he writes that indwelling sin so powerfully works to disorder and suppress this instinct that some “deal with their own children as a good man would not be hired with any reward to deal with his dog” (Works of John Owen, VI, 306).
But we can go beyond Owen's profound insights to simply note one more thing: Christian parents are the only parents who can be parents in the true sense of the word. While non-Christians feel the parental "law of operation" and provide for their children, Christian parents surpass the fulfillment of this basic impulse and see their parenting as part of their own obedience to God. The apostle Paul commands fathers "bring [their children] up in the discipline and instruction of the Lord" (Eph 6:4). This command is the revealed will of God for all people, but only those who live their lives in obedience to Him can fulfill it. Therefore Christian parents who live in obedience to this command are the only parents on the face of the earth who fulfill, not only the "law of operation" intrinsic to parenthood, but also their responsibility to God as the Creator to Whom they must give an account.