Watch this euphemism, as it just became the most important in the Obama administration's vocabulary now that the US has resumed air strikes in Iraq: force protection.

The F/A-18 strikes that the US launched Friday morning came with a rationale as plain as it was misleading – or, viewing it through the lens of Iraq's complicated diplomacy, usefully ambiguous for America's aims.

"To stop the advance on Irbil, I've directed our military to take targeted strikes against ISIL terrorist convoys should they move toward the city. We intend to stay vigilant, and take action if these terrorist forces threaten our personnel or facilities anywhere in Iraq, including our consulate in Irbil and our embassy in Baghdad," Barack Obama said in a statement from the White House late Thursday.

A more precise rationale becomes visible when you consider both where the strikes took place and where, months after Isis upended Iraq's fragile post-Saddam status quo, they haven't.

The two fighter jets hit a target outside of Irbil, the capital of Iraqi Kurdistan, an autonomous region notable both for its consistent embrace of the United States and for its stability throughout 11 years of war. The target was mobile Isis artillery that had been shelling Kurdish Peshmerga who have fallen back to defend the city where, Pentagon press secretary Rear Admiral John Kirby noted, "US personnel are located."

Those US personnel are among the special-operations advisers and diplomats Obama deployed for a "joint operations center" in Irbil. There, they assess and plan, with the Kurds – usually just referred to as Iraqis, another useful ambiguity – options for stopping Isis' advance. Until this week, few thought Kurdistan was at risk of falling to Isis. Now that's a real possibility. Out come the laser-guided bombs for the first air strikes Obama has ordered in Iraq since the 2011 withdrawal. A second round of strikes began Friday evening local time, including the first US drone strike in Iraq since 2011.

Yet the Obama administration faces a significant constraint in declaring a threat to Iraqi Kurdistan a threat to US interests. American diplomats are attempting to stitch together a new and ostensibly more inclusive government in Baghdad. For months, Obama has resisted Baghdad's entreaties to launch airstrikes against Isis. Arab Iraqi politicians can be forgiven for wondering why the US is unwilling to fly Super Hornets from the deck of the USS George HW Bush to defend their interests.

Citing a need to protect US forces in Irbil, then, is a convenient elision. Isis finds that the US is willing to attack its forces as they assault Iraqi Kurdish positions. The US gets to avoid, or at least defer, explicit preferential treatment for the Kurds, since protecting US forces is unambiguously a US necessity. Conspicuously, the US has yet to attack the Isis positions threatening Iraqi Yazidis at Mount Sinjar, whose dire conditions ostensibly prompted Obama's first step toward making the Iraq crisis an American one.

On the ground by Irbil, these distinctions are less meaningful. The F/A-18s might not have explicitly provided close air support for the Peshmerga – that would require coordination between the Peshmerga and the US Navy pilots – but the strikes nevertheless provide the Peshmerga with a measure of air cover, an advantage over the better-armored Isis fighters. It rhymes with close air support, at least: the Kurds get a chance to fortify the defense of Irbil.

Whatever their fears about the Yazidis' humanitarian emergency, Obama administration officials this week have been deeply worried by the vulnerability of Kurdistan. If Kurdistan falls, the war is transformed. The last unambiguously pro-US bastion of Iraq will be gone. Nato ally Turkey will face increased vulnerability to Isis. Baghdad's fractious politics will lose a moderating force, and the US will lose an extraction point of last resort should Baghdad fall. Isis will be at Iran's mountainous doorstep. The much-persecuted Kurds would be at risk of a new bloodbath. Quietly, there are calls for the US to funnel weapons to the Peshmerga; expect them to intensify.

Ever since Obama and Nato launched an air- and sea-based assault on Muammar Gaddafi's Libya in 2011, observers worldwide have wondered Why There And Not Elsewhere. Obama administration officials, including the many "strategic communications" specialists in the government, have struggled for three years to answer that question. They want to avoid entangling the US in yet another bloody Middle Eastern war that does not lend itself to American solutions. That extremely understandable reluctance has been consistently put to the test by adversaries – from Bashar al-Assad to Isis – who want to explore Obama's threshold of pain.

In the days and weeks ahead in Iraq, Obama will have to decide where his threshold is. If Isis cannot cross into Kurdistan, will Obama use air power to help the Peshmerga take back territory from Isis, a challenge Isis has never faced since it took Mosul in June? Will he bomb Isis positions crossing into Baghdad? The downside of war-by-euphemism is that it leaves actual US goals ambiguous to both allies and adversaries, and encourages strategic improvisation – the first step in mission creep.

After all, there are hundreds of US special operations "advisers" in Baghdad as well, all of whom may increasingly need aerial protection.