Over the past decade, the foreign-policy debate in Washington has turned upside down. As George W. Bush’s administration drew to an end, the brand of ambitious, expensive, Manichaean, militaristic foreign policy commonly dubbed “neoconservative” seemed on the verge of collapse. In December 2006, the Iraq Study Group, which included such Republican eminences as James Baker, Lawrence Eagleburger, Ed Meese, and Alan Simpson, repudiated Bush’s core approach to the Middle East. The group not only called for the withdrawal from Iraq by early 2008 of all U.S. combat troops not necessary for force protection. It also proposed that the United States begin a “diplomatic dialogue, without preconditions,” with the government of Iran, which Bush had included in his “axis of evil,” and that it make the Arab-Israeli peace process, long scorned by hawks, a priority. Other prominent Republicans defected too. Senator Gordon Smith of Oregon called the president’s Iraq policy “absurd” if not “criminal.” George Will, the dean of conservative columnists, deemed neoconservatism a “spectacularly misnamed radicalism” that true conservatives should disdain.

That was then. Today, hawkishness is the hottest thing on the American right. With the exception of Rand Paul, the GOP presidential contenders are vying to take the most aggressive stance against Iran and the Islamic State, or ISIS. The most celebrated freshman Republican senator is Tom Cotton, who gained fame with a letter to Iran’s leaders warning that the United States might not abide by a nuclear deal. According to recent polls, GOP voters now see national security as more important than either cultural issues or the economy. More than three-quarters of Republicans want American ground troops to fight ISIS in Iraq, and a plurality says that stopping Iran’s nuclear program requires an immediate military strike.

What explains the change? Above all, it’s the legend of the surge. The legend goes something like this: By sending more troops to Iraq in 2007, George W. Bush finally won the Iraq War. Then Barack Obama, by withdrawing U.S. troops, lost it. Because of Obama’s troop withdrawal, and his general refusal to exercise American power, Iraq collapsed, ISIS rose, and the Middle East fell apart. “We had it won, thanks to the surge,” Senator John McCain declared last September. “The problems we face in Iraq today,” Louisiana Governor Bobby Jindal argued in May, “I don’t think were because of President Bush’s strength, but rather have come about because of President Obama’s weakness.”

For today’s GOP leaders, this story line has squelched the doubts about the Iraq invasion that a decade ago threatened to transform conservative foreign policy. The legend of the surge has become this era’s equivalent of the legend that America was winning in Vietnam until, in the words of Richard Nixon’s former defense secretary Melvin Laird, “Congress snatched defeat from the jaws of victory by cutting off funding for our ally in 1975.” In the late 1970s, the legend of the congressional cutoff—and it was a legend; Congress reduced but never cut off South Vietnam’s aid—spurred the hawkish revival that helped elect Ronald Reagan. As we approach 2016, the legend of the surge is playing a similar role. Which is why it’s so important to understand that the legend is wrong.

By 2006, three years after American troops deposed Saddam Hussein, the situation in Iraq had grown terrifying. Violence had begun with a largely Sunni insurgency against the American occupiers and the Shia Muslims they had brought to power. But after Sunni jihadists bombed a famous Shia mosque in Samarra that February, Shia militias retaliated, sparking wholesale slaughter across the sectarian divide. The Tigris River became so clogged with human corpses that some Iraqis stopped eating its fish, believing their taste had changed.

In January 2007, Bush responded to these horrors not by withdrawing U.S. troops, but by sending 30,000 more. He also redirected U.S. military strategy. Under the leadership of General David Petraeus, U.S. troops began focusing less on killing insurgents and more on protecting Iraqi civilians, in hopes of reducing the insecurity that allowed the insurgency to thrive. American troops, working alongside Iraqi ones, went to live among the Iraqi people.

Fortuitously, these changes coincided with a shift among some Sunni leaders. By 2007, many had grown alienated by the harsh fanaticism of the al-Qaeda jihadists who had taken up residence in their midst. More important, some Sunni leaders realized that they could not defeat the more numerous Shia. Driven out of large sections of Baghdad, they came to see American troops as the only force capable of saving them.

In a daring about-face, Petraeus’s forces began paying the very Sunnis who had once fought Americans to fight al-Qaeda instead. That August, seeing a drop in Sunni attacks, the Shia militia leader Moqtada al-Sadr agreed to a cease-fire. The decline in violence was astonishing: In 2007, the war took the lives of 26,000 Iraqi civilians. In 2008, that number fell to just over 10,000. By 2009, it was down to about 5,000. When Republicans today claim that the surge succeeded—and that with it Bush won the war—this is what they mean.

But they forget something crucial. The surge was not intended merely to reduce violence. Reducing violence was a means to a larger goal: political reconciliation. Only when Iraq’s Sunni and Shia Arabs and its Kurds all felt represented by the government would the country be safe from civil war. As a senior administration official told journalists the day Bush announced the surge, “The purpose of all this is to get the violence in Baghdad down, get control of the situation and the sectarian violence, because now, without it, the reconciliation that everybody knows in the long term is the key to getting security in the country—the reconciliation will not happen.”

But although the violence went down, the reconciliation never occurred. According to the legend of the surge, Iraq’s collapse stems from Obama’s decision to withdraw all U.S. troops at the end of 2011. “If we’d had a residual force of 10,000 to 12,000,” Senator Lindsey Graham said last year, “I am totally convinced there would not have been a rise of al-Qaeda.” In reality, the prime minister of Iraq, Nouri al-Maliki, began persecuting the Sunnis—thus laying the groundwork for their embrace of ISIS—long before American troops departed the country. As early as 2007, writes Emma Sky, who advised both Petraeus and his successor, General Ray Odierno, “the U.S. military was frustrated by what they viewed as the schemes of Maliki and his inner circle to actively sabotage our efforts to draw Sunnis out of the insurgency.” In August 2008, Shawn Brimley and Colin Kahl, then affiliated with the Center for a New American Security, warned:

There is a gathering storm on Iraq’s horizon. Over the last several weeks, its central government has embarked on what appears to be an effort to arrest, drive away or otherwise intimidate tens of thousands of Sunni security volunteers … If Iraqi Prime Minister Nouri Maliki and his advisors persist in this sectarian agenda, the country may spiral back into chaos.

The tragedy of post-surge Iraq has its roots in America’s failure to make the Iraqi government more inclusive—a failure that began under Bush and deepened under Obama. In 2010, Sunnis, who had largely boycotted Iraq’s 2005 elections, helped give a mixed Shia-Sunni bloc called Iraqiya two more seats in parliament than Maliki’s party won. But the Obama administration helped Maliki retain power. And Obama publicly praised him for “ensuring a strong, prosperous, inclusive, and democratic Iraq” even after he tried to arrest his vice president and other prominent Sunni leaders.

These errors came well before Obama’s decision to remove American troops at the end of 2011. The fact is, the U.S. failed to stop Maliki’s slide into sectarian tyranny even when it still had 100,000 troops patrolling Iraqi soil. That’s because America had already lost much of its leverage. Once the surge succeeded in reducing violence, Maliki no longer needed American troops to keep him in power. By 2010, U.S. aid to Iraq had dropped dramatically. Iraq was buying American weapons, but had the oil revenue to buy them elsewhere if America stopped selling. And the Obama administration could not pressure Maliki by threatening to withdraw U.S. troops, because Maliki wanted them gone. So did most of the Iraqi people.

The problem with the legend of the surge is that it reproduces the very hubris that led America into Iraq in the first place. In 2003, the Bush administration believed it could shatter the Iraqi state and then quickly and cheaply construct a new one that was stable, liberal, democratic, and loyal to the United States. By 2006, many conservatives had realized that was a fantasy. They had massively overestimated America’s wisdom and power, and so they began groping for a new approach to the world. But then, in 2007 and 2008, through a series of bold innovations, the United States military bribed, cajoled, and bludgeoned Iraqis into multiple cease-fires. The Iraqi state was still broken; its new ruling elite showed little of the political magnanimity necessary to reconstruct it in an inclusive fashion. And the Band-Aids that Petraeus and his troops had courageously affixed began peeling off almost immediately. Nonetheless, Republicans today say the Iraq War was won, and would have remained won, had the U.S. left 10,000 troops in the country after 2011.

How much damage will the GOP’s revived hubris do? Inconceivable as it would have seemed a few years ago, Graham, who is now a Republican presidential hopeful, has suggested sending 10,000 American ground troops back into Iraq. (His GOP rivals generally support this idea but have not proposed exact troop numbers.) The U.S. is unlikely to send a sizable American ground force back into Iraq. But this line of thinking is troubling nonetheless, because the same wild overestimation of American power that fueled the war in Iraq now fuels the right’s opposition to the nuclear deal with Iran. To hear hawks tell it, the United States can scuttle the current deal, intensify sanctions, threaten war, and—presto—Tehran will capitulate. But Iranians have been living under the threat of attacks from America or Israel for more than a decade now. And British and German diplomats have warned that if the U.S. Congress torpedoes the agreement, sanctions pressure on Iran will go not up but down, as countries that have lost billions by limiting their trade with Tehran stop doing so.

One day, Republicans will resume the painful work they began in 2006—the work of reconciling conservative attitudes with the limits of American power. Let’s hope they don’t do too much damage before that day comes.