An ISIS fighter at a checkpoint near the city of Baiji, north of Baghdad, on June 19. REUTERS/Stringer On Thursday night, President Barack Obama authorized the use of U.S. military strikes in Iraq, wading the U.S. further into the conflict that has, in recent days, pitted insurgents from the Islamic State of Iraq and the Levant (ISIS) against Kurds in the northern region of the country.

But there's an inescapable paradox that explains, in part, how ISIS insurgents have been able to make sweeping advances toward the Kurdish capital against the peshmerga, Iraq's most formidable military force.

ISIS is using modern U.S. weapons its fighters have seized from Iraqi forces, while the Kurds fight with Soviet arms.

"They are literally outgunned by an ISIS that is fighting with hundreds of millions of dollars of U.S. military equipment seized from the Iraqi Army who abandoned it," Ali Khedery, a former American official who has served as an adviser to five U.S. ambassadors and several American generals in Iraq, told The New York Times.

McClatchy reports that the Kurdish peshmerga, meanwhile, possess "a handful of 12.7mm Soviet-era heavy machine guns and rocket-propelled grenades," along with a few Soviet-era T-55 tanks, to take on battle-hardened militants riding in U.S. Humvees.

The most recent gains by ISIS — which has a disciplined military command — have exposed the key weakness of the well-trained but ill-equipped peshmerga while presenting the U.S. with a challenge if the Obama administration wants to to limit its involvement in the fight.

The tragic irony: there's more reason to remove ISIS from Iraq than there was to overthrow Saddam Hussein — ian bremmer (@ianbremmer) August 8, 2014

The U.S. has not decided whether to arm the peshmerga. Michael Knights of the Washington Institute says there are a bunch of other ways that America could bolster the peshmerga, including operational and intelligence support, airpower, logistics, and training.

And if the U.S. doesn't bolster the peshmerga, one of America's historic allies may be overrun by terrorists using U.S.-made equipment.

[UPDATE 9:10 EDT] The U.S. has conducted an airstrike on ISIS artillery that was used against the Kurds near Erbil, signaling an assertive U.S. posture against ISIS. Nevertheless, air strikes will have to be part of a comprehensive plan.

"Air strikes are very much needed to support both the Kurds and the government in Baghdad, but in the end the fighting will come down to ground troops against ISIS," Garrett Khoury, the director of research at The Eastern Project, told Business Insider in an email. "Both the Kurds and the main Iraqi military need proper training and equipment if they are going to be in any way successful."