The violent riots and cold-blooded killing of two US military advisers Thursday by an Afghan soldier upset over the US military’s burning of Qurans are raising increasingly urgent questions among troops about whether mission in Afghanistan is worth it – both in the cost of nearly 2,000 American lives and the billions of dollars that the cash-strapped US has poured into the country.

For many, the question is one of gratitude. Though the Pentagon says the burning may have been a mistaken attempt to destroy books in which prisoners were passing extremist messages, rioting Afghan crowds are still chanting "Death to America." Does the act of burning Qurans really overshadow all the "blood and treasure" America has spent in Afghanistan?

Even for others, who are inclined to be more sensitive to the deep offense created by burning Qurans, the past two weeks have been troubling. When Afghan President Hamid Karzai feels no need to apologize for a member of the Afghan Army killing two Americans, it is a sign of a perhaps irrevocably broken partnership, says retired Col. Peter Mansoor, former executive officer to Gen. David Petraeus during the height of the insurgency in Iraq.

“If it’s not a true partnership, then why should we sacrifice American blood and treasure?” says Colonel Mansoor, who is now a professor of military history at Ohio State in Columbus. "Americans have cultural sensitivities, too. Maybe we’re so sensitive to Afghan culture that we’re forgetting our own.”

On both sides, the signs of strain from 10 years of war are growing. Afghans see the Quran burnings as merely the latest sign that the foreign soldiers in their land do not share or care for their culture or beliefs. Americans wonder why they are not lauded for risking their lives for the security of another country.

Lost in the sense of ill-usage, however, is the idea that troops are sent to war not to collect plaudits, but rather to defend some vital US national security interest, says Kimberly Kagan, president of the Institute for the Study of War, a Washington think tank, and an adviser to US commanders in Afghanistan.

“It would be wonderful if out of this experience, the soldiers come to love the Afghan people, and the Afghan people come to love us,” she says. But “we’re not in Afghanistan in order for the Afghans to say thanks to us. We’re there because we have core interests in Afghanistan.”

Asking for thanks, she suggests, can reek of imperialism or even racism, with the foreign force seeing itself as beneficently saving a people from itself.

For Mansoor, however, the issue is not one of gratitude, but mutual respect.

“We can understand the protests – Karzai doesn’t have to apologize for that,” Mansoor says. He says he can also understand resentments of everyday Afghans who sometimes see American forces as occupiers.

“But when Afghan soldiers take guns out and shoot Americans in the back of the head? These people are in the employ of the Afghan government,” he adds. “President Karzai should give Americans a loud and public apology.”

“Yes, we inadvertently burned Qurans, but it was a mistake. It wasn’t intentional. We weren’t saying, ‘Screw Islam,’ ” he says.

Such an apology comes with political risks – as President Obama learned when he issued one of his own in the wake of the Quran burnings. Republican presidential candidates rushed to be the first to condemn it.

“I think for a lot of people, that sticks in their throat,” Mitt Romney told Fox News. “We’ve made an enormous contribution to help the people there achieve freedom, and for us to be apologizing at a time like this is something which is very difficult for the American people to countenance.”

Newt Gingrich likened the apology to a surrender. If Mr. Karzai “doesn’t feel like apologizing” for the killing of US soldiers by Afghans, “then we should say, 'Goodbye and good luck, and we don’t need to be here risking our lives and wasting our money on somebody who doesn’t care.' ”

Those same political risks echo in Afghanistan, too. For an Afghan public weary of war and, increasingly, of the American presence, a Karzai apology could seem intolerably weak. Moreover, in a society that doesn't shy away from violence to settle perceived injustices – and where the burning of the Quran is a grievous blasphemy – an apology could run starkly against the public mood.

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The reaction by the Afghan government in the wake of violence toward US troops, however, has made officials like Mansoor question America’s war there.

In 2010, Mansoor traveled to Afghanistan and “I was pretty high on what we were doing,” he says. But today, regardless of current US troop levels in the country, among Afghans “the feeling of ingratitude runs pretty deep. I mean, Karzai is a disappointment. He’s pandering to his base. And, as a result, he might lose the war.”