Barzani explains why the Islamic State is a formidable adversary: Its best weapons are car bombs; it sent 14 of them against Kurdish lines one day last month. The hardened fighters, many from such places as Chechnya, Kazakhstan and Uzbekistan, blow themselves up rather than surrender. Suicide bombers who think they’re about to meet virgins in heaven are dubbed “grooms.”

But the jihadists have internal problems, too. The foreign fighters, who are called “muhajiroun,” the Arabic word for emigrants, get the pick of captured women and money. The local fighters, known as the “ansar,” are resentful. The jihadists are so nervous about traitors that anyone leaving Mosul is asked to designate a hostage who will be killed if he doesn’t come back. Panicky Islamic State fighters fleeing a battle were told they would be shot if they reached an Islamic State base in Tal Afar.

The United States is counting on the Kurds to hold their ground against these killers while other Iraqi forces get trained. And that brings Barzani to his most important point: The Kurds need U.S. weapons, fast. In particular, they need armored personnel carriers and Humvees to protect their troops, tanks to repel enemy advances, night-vision goggles to detect sneak attacks and small attack helicopters to defend a front that stretches 600 miles.