"Come, talk to me, too," he said.
He introduced himself as Louay Hikmat Shawkat, Iraqi Army veteran of the war with Iran and then the 1991 Kuwait war, refugee from Mosul and a self-described translator of English, French, "Canadian" and "Yugoslavian."
Given that the latter two aren't languages, and his English was a tad scratchy, I was intrigued.
We were visiting the school to talk to its current "residents" -- 48 Christian families who had fled Mosul when ISIS took over a year ago. Mosul, in northern Iraq and one of the nation's largest cities, is about 405 kilometers (about 250 miles) from the capital of Baghdad. But for these internal refugees, it might as well be a world away.
I asked Louay, who is 60, when he thought he might be able to return home.
ISIS 'is an illness ... impossible to cure'
"Take it out of your mind that ISIS is going to leave Mosul," he insisted, gesturing with his hand as if he were pulling a thread out of his head.
The chances he and his wife will someday return to their home in the Mosul suburb of Hamdaniya, he said, are "one in a hundred. One in a million!"
Louay said he suffers from diabetes, but he insists on lighting up another cigarette in his nicotine-stained fingers "because I get upset whenever I speak about "Da'ish", the Arabic acronym for ISIS.
ISIS, he said, "is an illness. It's impossible to cure. Cancer can be cured, tuberculosis can be cured. Almost every illness can be cured, but not this one."
His diabetes causes him to suffer from dizziness whenever he stands up. "If I were well," he vows, "I would go fight them myself."
Like everyone else I spoke with at the school, he is desperate to leave Iraq, but his attempts to apply for asylum have come to naught. His last hope, he told me with a mischievous grin, is an old Canadian girlfriend in Montreal.
Another Mosul refugee: 'We are finished'
In the school's makeshift kitchen, I met Linda Jannan, who was busy with the washing up.
She fled Mosul with her husband and three children in August, first going to Dohuk, in Iraqi Kurdistan, where they spent six months in a tent in a refugee camp.
A thin women in her 30s with the dark circles under her eyes, she also was desperate to leave Iraq.
"We are finished," she told me. "Our future, our children, our men have been destroyed. We're too afraid to go out and find work. If only someone outside Iraq will help us find a solution, let us emigrate. We have no hope left."
She and her husband had applied to asylum in the United States and Germany, but they were rejected because they have no close relatives in either country.
Over the past few months, these refugees have been visited by a variety of reporters. And it's clear their patience is wearing thin.
"What's the point of all this talk?" one man asked me, after declining my request for an on-camera interview. "We talk, we talk, and nothing happens," he snapped.
Firyal Abdel Kareem, who was sharing the kitchen with Linda Jannan, is at her wits' end. She spent the winter months in a windy tent in Zakho, near the Turkish border, and is now suffering from Baghdad's sweltering summer heat.
"Find a solution for us," she told me, "it's enough. We are tired."
"Either they take us out of here, or send us home. Do we have to stay in this school, or in a tent?"
Mired forever in a terrible situation
I've been covering Iraq since 1994. I covered the impact of the draconian international sanctions imposed on the country after Iraq's 1990 invasion of Kuwait. I covered the U.S.-led invasion in 2003 and the messy, bloody aftermath. And now I'm back covering the war against ISIS.
I'm lucky. I come and go as I please. For the people in this school, there is no such luxury. Thair Al-Naim, his wife and their three young sons left behind a relatively comfortable life in Mosul last summer. He's now penniless and out of work, all his construction equipment seized and sold by ISIS.
Speaking to him in the classroom they now call "home," I sense a deep weariness with a life that, for too long, has been fraught with violence and fear.
"Since the fall of Saddam," he sighs, "all we've had is war after war, and now we have Da'ish."