Yes, that is the flaw in my reasoning. If someone used my reasoning to just check out and not be concerned about their children being abducted, then we'd rightly believe there is something wrong with that person.
And if the parent became manic and left no stone unturned in their search for their child, like Taken, we'd be understanding.
Yet, our world is not the world of Taken, and we are not ex-CIA agents capable of destroying anyone in our path. There are truly evil people in this world capable of harming us, whom we have no power to thwart. Think of people living in the land of a drug lord, who can swoop in and take their children if he feels like it. Or the Uighurs and Falun Gong of China, who are regularly captured and organ harvested, and there's nothing they can do about it. There is great evil in our world, and little we can do about it but do our best to fight it and never give up, and even then there is no hope of truly eradicating evil from our world. What is the appropriate response?