The moment of truth on Iraq is coming at summer’s end, when Lieutenant General David Petraeus is expected to tell the nation how long American forces must fight.

For those who were listening, however, the top commander of American troops has already said it generally takes 10 years to put down an insurgency such as the one facing his troops. The more relevant question about Iraq therefore is not “how long?” but “why stay?”

Perhaps a process of elimination would be helpful:

1) Preventing a civil war among Iraqis is not a reason. That war is well under way among Iraqi Shiites and Sunnis and is certain to spread to the Kurdish territories once the Shiites, who represent 70% of Iraq’s population, prevail. The inescapable facts of sociology, geography, and political leadership in the Persian Gulf are that Iran, the dominant power in the region, has a population of 75 million Shiites who have a natural bond with their 20 million brethren in Iraq; Iran and Iraq share a very long border, and Iran has an unlimited supply of arms and money and, most importantly, the patience to let time work to its advantage.

We have seen enough of how things work in the Middle East throughout the last century to understand that the bloodletting will not settle down for many years to come. Sadly, it matters very little how many American troops die in securing a Sunni neighborhood here or a Shiite one there or, eventually, a Kurdish enclave in the North. The genie of ethnic-tribal wars, already on the loose from Turkey to Lebanon, will pursue its natural course. A wise leader cannot ask American forces to arbitrate blood wars indefinitely.

2) Staying in Iraq to prevent Al Qaeda from nesting there is not a reason. True, Al Qaeda has manifested itself in Iraq in unmistakable ways, as it has in Lebanon, Somalia, Pakistan, Gaza, and among generations of Pakistani immigrants to Britain. But the reality is that what started as Osama bin Laden’s project of building an Islamic terror “base” (the Arabic meaning of qaeda) has transcended its founder and become a state of mind among many Muslims in many different places.

Iraq is only one those places. Fighting the Al Qaeda of today requires a fresh Western strategy that recognizes the enemy as a moving target operating on several terrains — including among Muslim communities long settled in the West itself.

3) Preventing the region as a whole — including such strategic oil assets as Saudi Arabia and the smaller emirates of the Persian Gulf, as well as more distant countries like Lebanon and Israel — from facing unrelenting pressure from Iranian-inspired forces is not a reason. Advocates of a continued fight in Iraq correctly argue that, if America pulls out of Iraq, this would, indeed, occur. But far more relevant is that such pressure is already being applied, despite the presence of 140,000 American soldiers in Iraq.

4) Finally, staying in order to give the American military the opportunity to “win” is not a reason. The prospect of staying the course in Iraq in any major configuration is firmly rejected by the American people in poll after poll. No amount of political maneuvering or spin can disguise this. If the long, painful Vietnam conflict proved anything, it is that the armies of a great democracy cannot fight without support at home. There is no need to await demonstrations in the streets.

As was clear before and after the attacks of September 11, 2001, the root causes of this untenable situation are endemic to Islam and its collision with the failed states that propagate it, such as Saudi Arabia and Pakistan. Hundreds of Saudi jihadists are returning from Iraq to fight against their own government at home; Al Qaeda-type groups are metastasizing all over the Islamic world, from Islamabad’s Red Mosque, where a long, bloody rebellion was quelled last week, to Palestinian refugee camps in Lebanon and Hamas and Palestinian Arab population centers in the West Bank. Even the best armies, as Israel discovered in Lebanon in the summer of 2006, are not the definitive answer in this fight.

America may have gone into Iraq in an unstudied, and probably misguided, manner — and many among us warned against rushing into it — but in its essence, the American project was a noble one. But it has now failed. A more urgent war — against jihadist Islam — beckons.