WASHINGTON – The most profound legacy of the American intervention in Iraq may be the way it changed the U.S. military’s understanding of war.

President Obama promised Friday that U.S. troops will have vacated the country by Christmas, effectively ending an occupation that claimed more than 4,400 American lives and stretched for nine years.

The Iraq war has long been plagued by its contradictions. It toppled a hostile dictator, but many Americans remain troubled that the conflict was launched on what proved to be the false contention that the country was developing weapons of mass destruction. Even within the U.S. military, there is no broad agreement that the war’s outcome is a victory.

The 2003 attack on Baghdad was premised on the idea that overwhelming American firepower could do extraordinary things. Precision bombs and American tanks, linked by new information technology, could liberate a country with little risk to U.S. forces.

With a little help from American troops and civilians, a new democracy could take root.

“Iraq reintroduced us to the ugliness of war,” said Matt Sherman, who spent three years in Iraq as a civilian adviser to the U.S. military.

Today, American soldiers and Marines parse their experiences in Iraq very finely. When they talk about Iraq, they rarely refer to a single war. Individuals tours are seen as separate conflicts, each with its own lessons.

The disparate experiences have triggered a roiling debate over precisely what lessons the American military should take from the different phases of the conflict.

Col. Gian Gentile led a U.S. cavalry squadron in western Baghdad during some of the war’s bleakest days in 2006. “I saw terrible things,” he said, describing an experience that was common and deeply affecting. “I had five soldiers killed and had 15 with life-changing wounds.”

He returned to the United States shortly before Gen. David Petraeus, guided by the new counterinsurgency doctrine that he had helped write, arrived in Iraq for his third combat tour. Petraeus’ counterinsurgency approach promised to turn the old American way of war on its head.

Instead of hammering the enemy, his new doctrine urged commanders to focus on protecting the Iraqi people and persuading them to support the Iraqi government.

“Some of the best weapons for counterinsurgency do not shoot,” the counterinsurgency manual counseled.

“Sometimes doing nothing is the best reaction,” it cautioned.

From the moment Gentile read it, he doubted its utility. “It was telling me that if I would have treated the population differently in Baghdad, then the outcome would have been different,” he said.

As violence in Baghdad dropped, U.S. military officers and politicians began proclaiming the success of the new approach. Gentile, who teaches history at the U.S. Military Academy, became one of the Army’s most strident heretics.

The intense, tactical focus on securing Iraqi neighborhoods in accordance with the new doctrine had prevented the U.S. military from asking big strategic questions about the war’s utility, Gentile argued.

“I hope we are going to start asking some of the hard questions now,” he said. “What have the last eight years really gotten us? What has military force really accomplished in Iraq?”

Retired Lt. Col. Doug Ollivant helped build and then implement Petraeus’ plan to protect Baghdad in 2007. The approach Ollivant advocated was drawn directly from the counterinsurgency doctrine that so disturbed Gentile.

U.S. battalions and companies moved into small, neighborhood outposts that they shared with Iraqi police and army units. Ollivant and his immediate commanders put the outposts on sectarian fault lines. The goal was to make it harder for warring Sunni and Shiite Muslims to kill each other.

During the first few months of the new strategy, American and Iraqi deaths spiked as insurgents focused their firepower on the newly vulnerable Americans. Then violence began to fall precipitously. The conclusion that swept through the Army in 2008 and 2009 was that Petraeus’s doctrine and leadership had reversed the course of the war.