NATO LEADERS gathering in Chicago on Sunday are all, in their own way, looking for the exit from Afghanistan. It’s understandable, after a decade of war. But it is safe to bet that the faster they rush out, the more they — or their successors — will regret.

The tone has been set, for good and ill, by President Obama. On the unfortunate side, he has set a schedule for troop withdrawal unrelated to military strategy or conditions on the ground. That is forcing Gen. John R. Allen, the supreme allied commander in Afghanistan, to withdraw forces from the south sooner than sound tactics would have dictated and to curtail an offensive in the east that is crucial to Kabul’s security.

On the positive side, Mr. Obama has promised that the United States will remain committed to Afghanistan’s success even after NATO troops end their combat mission at the end of 2014. With its allies, it will support Afghan development, train Afghan troops and conduct counterterrorism missions. It won’t abandon Afghanistan, in other words, as it did, to its eventual sorrow, after helping to drive the Soviets out in the late 1980s.

Americans and Europeans who question the need for such a commitment or want to pull out even faster than NATO has pledged, ask: Why does Afghanistan matter? Al-Qaeda is gone and could just as likely regroup in Yemen or Somalia or anywhere else. Afghanistan has no significance to the global economy and isn’t likely to anytime soon. The future is further east: Why not pivot to Asia now?

We would make, in part, a moral argument — that the allies bear some measure of responsibility to Afghan troops who have fought bravely alongside them and to Afghan women, to whom much has been soaringly promised. But the selfish, strategic arguments are more than sufficient.

It’s true that al-Qaeda and its affiliates will need to be fought, though not always in the same way, wherever they appear. But if the Taliban returns to Afghanistan, al-Qaeda surely will come back, too. Throw in the instability of nuclear Pakistan and tensions with neighbors such as Iran and the risks of leaving a security vacuum become intolerable. The sad fact is that a global leader doesn’t always get to choose its enemies, nor the regions of the world where it must be engaged. Neither do its allies if they want to remain relevant.

NATO has set its schedule for withdrawal from combat in Afghanistan. It is a risky course, but it is not doomed to fail. Afghan forces are improving. The Taliban remains unpopular, and infighting among its leaders reflects some stress. But if the NATO strategy is to have any chance, the allies cannot further accelerate their departure. They cannot succumb to wishful thinking about the likelihood of reconciliation with their enemies. And they cannot begin dismantling the Afghan forces, through shortsighted penny-pinching, before those forces have established themselves.