The tragedy unfolding in Iraq now—one that could turn that country’s death toll of nearly a thousand a month to five or ten times that number—is heartbreaking. We’ll get to that, and what might happen, in a minute. But let’s first take on the despicable hawks, neoconservatives and George W. types who make the argument—like the one made by David Brooks in The New York Times today, and which has been repeated over and over again since 2011 by the likes of John McCain, Lindsey Graham, Bill Kristol and others—that President Obama cavalierly abandoned Iraq three years ago, pulling out too soon and leaving Iraq to its own devices.

Here are the facts. After being elected in 2008, Obama tilted to the advice of his more hawkish advisers on Iraq. The relative doves that provided advice to Obama’s campaign, including people like Brian Katulis from the Center for American Progress, who’d supported a rapid drawdown of US forces, were eclipsed by those, such as Colin Kahl, who wanted a slow, cautious, step-by-step drawdown. Indeed, that’s what happened. And the Obama administration tried its best to work out a plan for a long-term US-Iraqi security agreement, such as the one it’s implementing in godforsaken Afghanistan now. But those negotiations failed. Ostensibly, they failed because of certain sticking points, such as the demand from the United States that Iraq provide legal immunity to US troops, which Iraqis felt was a violation of their national sovereignty. But the real reason that the talks stalled, and then collapsed, was because the Iraqis didn’t want the United States to stay. Not only did many Sunnis, who might have favored the United States as a stabilizing presence, say that America was an occupying power, but the government installed by George W. Bush and Co., heavily weighted toward extremist, sectarian Shiites with close ties to Iran, didn’t want the United States to stay either. And that’s partly because Iran, which has enormous influence in Baghdad—where its ambassadors are routinely drawn from the ranks of the Islamic Revolutionary Guard Corps (IRGC)—didn’t want any US role in Iraq, and Tehran made its wishes clear to Prime Minister Nouri al-Maliki in no uncertain terms. So, short of toppling Maliki, the United States was out. (It should be pointed out that many critics on the left, including me, opposed Obama’s efforts to maintain a US force in Iraq beyond 2011.)

Meanwhile, it was W.’s neocons, and idiots such as Paul Bremer, who after 2003 obliterated Iraq’s social, political and military institutions, dissolved the armed forces, destroyed the Baath party and handed power to sectarian Shiites and the Kurds. The fact that the Islamic State of Iraq and Syria (ISIS) can have the support that it appears to have in Sunni areas of Iraq—despite its brutal history of summary executions, beheadings and onerous social diktats—is the result of putting in place a sectarian, Iran-linked Shiite bloc that viewed all Sunnis as apostates and would-be terrorists.

So what we see today is the harvest of those errors, and they can’t be fixed now by the United States. (Indeed, if Iraq is able to cobble together forces to retake Mosul and Falluja in the next months and years, at great human cost on both sides, it will be because Iran intervenes in support of Maliki et al. There’s no role for the United States.)

Now, what’s happening in areas seized by ISIS is horrible: mass executions, threats to kill anyone who worked for the government, leaflets proclaiming that new social restrictions on women and free expression are imminent, and more. (Of course, Maliki’s government isn’t a whole lot better. And people are fleeing Mosul, at least 500,000 so far, because they fear brutal reprisals and air strikes by the Iraqi government, which is what has been happening further south in Anbar since 2013.)

There is a real danger that ISIS and its allies can set up a rump statelet in northwest Iraq and northern and eastern Syria controlled by ISIS, and its allies, including groups more closely affiliated to Al Qaeda. (Al Qaeda broke with ISIS because the latter group was too willing to kill Muslims, both Sunni and Shiite.) In fact, however, ISIS can’t hold Mosul for long, and it doesn’t have a prayer of capturing Baghdad—nor can it get anywhere near Najaf and Karbala, the Shiite holy cities. But threats by ISIS commanders targeting those two cities are designed to inflame Shiite fears, and so they have, including in Iran, which sends countless pilgrims to Najaf and Karbala every year. Already, Grand Ayatollah Ali al-Sistani, the Shiite chieftain and revered leader, is calling for a full Shiite mobilization, and undoubtedly Iran will be willing to help set up Shiite paramilitary groups in Iraq, if it isn’t already doing so. (Indeed, The Wall Street Journal reports that the head of Iran’s IRGC’s Quds Force is in Iraq, and that Iranian forces are already involved, but that’s not confirmed.)

The battle in Iraq is part of a regional conflict, with both sectarian and state-power dimensions, between Iran and Saudi Arabia. (Unfortunately, the United States seems to have sided with the Sunni and Saudi side in this battle, with catastrophic results in Syria.) The solution, therefore, lies in a regional détente and compact between Tehran and Riyadh. The United States, which otherwise ought to stay out of the fight, ought to encourage such a deal, though its influence is less than stellar at this point. In recent weeks, there have been signs that Tehran and Riyadh are trying to improve relations, which could stabilize Syria and Iraq and ease Saudi fears of a US-Iran nuclear accord.

For Iran, which styles itself as the leader of the world’s Shiites, ISIS is a grave threat. Saudi Arabia, all too willing to mobilize Sunni fighters against Shiites in Iraq and Alawites in Syria, may be beginning to realize that ISIS (and Al Qaeda) could threaten Saudi Arabia too, and that things have gone too far. (Pakistan, which supports jihadists in every direction, seems never to have figured this out.) It’s possible to imagine Saudi Arabia and Iran agreeing on what to do in Syria, and in Iraq, though a hell of a lot more people might have to die first.

So far, there’s no reason to suspect that ISIS has the United States in its sights. Indeed, ISIS ought to be grateful to Washington for American support for the jihad in Syria against President Bashar al-Assad. So, by staying out of Iraq the United States will lessen the likelihood that ISIS will turn against Washington, and use terrorist attacks to make its point. That’s a big incentive not to use US airstrikes against ISIS positions, as Maliki has called for, and let’s hope that the CIA and the Pentagon keep their drones elsewhere, too. Striking ISIS will just give radicals there more reason to target the United States, and certainly won’t be effective in destroying a regional movement with plenty of money and support—and lots of US weapons that they’ve captured in Mosul and elsewhere.