Photograph by James Glover/Reuters

The exchange started like this: at the end of Jeb Bush’s town-hall meeting in Reno, Nevada, on Wednesday, a college student named Ivy Ziedrich stood up and said that she had heard Bush blame the growth of ISIS on President Obama, in particular on his decision to withdraw American troops from Iraq in 2011. The origins of ISIS, Ziedrich said, lay in the decision by Bush’s brother, in 2003, to disband the Iraqi Army following the toppling of Saddam Hussein’s government.

“It was when thirty thousand individuals who were part of the Iraqi military were forced out—they had no employment, they had no income, and they were left with access to all of the same arms and weapons.… Your brother created ISIS,’’ she said.

“All right,’’ Bush said. “Is that a question?”

“You don’t need to be pedantic to me, sir,” she said.

“Pedantic? Wow,” Bush said.

Ziedrich finally came forth with her query: “Why are you saying that ISIS was created by us not having a presence in the Middle East when it’s pointless wars, where we send young American men to die for the idea of American exceptionalism? Why are you spouting nationalist rhetoric to get us involved in more wars?”

Jeb replied by repeating his earlier criticism of President Obama: that Iraq had been stable until American troops had departed. “When we left Iraq, security had been arranged,” Bush said. The removal of American troops had created a security vacuum that ISIS exploited. “The result was the opposite occurred. Immediately, that void was filled.”

“Your brother created ISIS” is the kind of sound bite that grabs our attention, because it’s obviously false yet oddly rings true. Bush didn’t like it: he offered a retort and then left the stage. Meanwhile, Ziedrich had started a conversation that rippled across Twitter, Facebook, and any number of American dinner tables. Who is actually right?

Here is what happened: In 2003, the U.S. military, on orders of President Bush, invaded Iraq, and nineteen days later threw out Saddam’s government. A few days after that, President Bush or someone in his Administration decreed the dissolution of the Iraqi Army. This decision didn’t throw “thirty thousand individuals” out of a job, as Ziedrich said—the number was closer to ten times that. Overnight, at least two hundred and fifty thousand Iraqi men—armed, angry, and with military training—were suddenly humiliated and out of work.

This was probably the single most catastrophic decision of the American venture in Iraq. In a stroke, the Administration helped enable the creation of the Iraqi insurgency. Bush Administration officials involved in the decision—like Paul Bremer and Walter Slocombe—argued that they were effectively ratifying the reality that the Iraqi Army had already disintegrated.

This was manifestly not true. I talked to American military commanders who told me that leaders of entire Iraqi divisions (a division has roughly ten thousand troops) had come to them for instructions and expressed a willingness to coöperate. In fact, many American commanders argued vehemently at the time that the Iraqi military should be kept intact—that disbanding it would turn too many angry young men against the United States. But the Bush White House went ahead.

Many of those suddenly unemployed Iraqi soldiers took up arms against the United States. We’ll never know for sure how many Iraqis would have stayed in the Iraqi Army—and stayed peaceful—had it remained intact. But the evidence is overwhelming that former Iraqi soldiers formed the foundation of the insurgency.

On this point, although she understated the numbers, Ziedrich was exactly right. But how did the dissolution of the Iraqi Army lead to the creation of ISIS?

During the course of the war, Al Qaeda in Iraq grew to be the most powerful wing of the insurgency, as well as the most violent and the most psychotic. They drove truck bombs into mosques and weddings and beheaded their prisoners. But, by the time the last American soldiers had departed, in 2011, the Islamic State of Iraq, as it was then calling itself, was in a state of near-total defeat. The combination of the Iraqi-led “awakening,” along with persistent American pressure, had decimated the group and pushed them into a handful of enclaves.

Indeed, by 2011 the situation in Iraq—as former Governor Bush said—was relatively stable. “Relatively” is the key word here. Iraq was still a violent place, but nowhere near as violent as it had been. The Iraqi government was being run by Prime Minister Nuri al-Maliki, a fervent Al Qaeda foe and ostensible American ally.

But, as the last Americans left Iraq, there came the great uprising in Syria that pitted the country’s vast Sunni majority against the ruthless regime of Bashar al-Assad. Syria quickly dissolved into anarchy. Desperate and seeing an opportunity, Abu Bakr al-Baghdadi, the leader of the Islamic State of Iraq, dispatched a handful of soldiers to Syria, where, in a matter of months, they had gathered an army of followers and had begun attacking the Assad regime. Suddenly, Baghdadi’s group—which had been staggering toward the grave only months before—was regaining strength. In 2013, the I.S.I. became the Islamic State of Iraq in Syria. ISIS was born.

Finally, in June, 2014, legions of ISIS fighters swept out of Syria and grabbed huge swathes of northern and western Iraq. That prompted President Obama to order American troops to help save the Iraqi Army—indeed, to help save Iraq itself—and American pilots to bomb ISIS’s positions. Baghdadi, in proclaiming himself the caliph of the Islamic State, had assembled around himself a group of leaders, many of whom were once soldiers in Saddam Hussein’s Iraqi Army.

In this sense, Ziedrich is right again, at least notionally: some of the men fighting in ISIS were put out of work by the American occupiers in 2003. Still, it’s not clear—and it will never be clear—how many of these Iraqis might have remained peaceful had the Americans kept the Iraqi Army intact. One of the Iraqis closest to Baghdadi was Ibrahim Izzat al-Douri, a senior official in Saddam’s government until 2003. (Douri was reported killed last month—it’s still not clear if he was or not.) It’s hard to imagine that Douri—or any other hardcore member of Saddam’s Baath Party—would have ever willingly taken part in an American occupation, whether he had a job or not. So, in this sense, Ziedrich is overstating the case. While it’s true that George W. Bush took actions that helped enable the creation of the Iraqi insurgency, and that some leaders of the insurgency formed ISIS, it’s not true that he “created” ISIS. And there’s a good argument to be made that an insurgency would have formed following the invasion of Iraq even if President Bush had kept the Iraqi Army together. He just helped to make the insurgency bigger.

But let’s get to Governor Bush’s assertion—that Iraq went down the tubes because of President Obama’s decision to pull out all American forces, and that Obama could easily have left behind a residual force that would have kept the peace.

I took up this issue last year in a Profile of Maliki, the Iraqi leader we left in place. Maliki didn’t really want any Americans to stay in Iraq, and Obama didn’t, either. But—and this is a crucial point—it seems possible that, if Obama had pushed Maliki harder, the United States could have retained a small force of soldiers there in noncombat roles. More than a few Americans and Iraqis told me this. They blame Obama for not trying harder. “You just had this policy vacuum and this apathy,” Michael Barbero, the commander of American forces in Iraq in 2011, told me, describing the Obama White House.