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(CBS) It's an offense punishable by death during wartime. It's been committed by 5500 soldiers since the war with Iraq began.

The men, who have violated military orders and oaths, tell 60 Minutes Wednesday that it isn't cowardice, but rather the nature of the war in Iraq, that turned them into American deserters.

American soldiers currently living in Canada tell Correspondent Scott Pelley why they made the decision to desert their units, in a report to be broadcast on Dec. 8, at 8 p.m. ET/PT.

One soldier, Pfc. Dan Felushko, 24, tells Pelley, "I didn't want...'Died deluded in Iraq' over my gravestone."

It was Felushko's responsibility to go with the Marines to Kuwait in January 2003. Instead, Felushko slipped out of Camp Pendleton, Calif., and deployed himself to Canada.

"I was a warrior...I always have been," Felushko tells Pelley. "I've always felt...that if there are people who can't defend themselves, it's my responsibility to do that."

"As we're sitting here, something just short of 1100 Americans have died. What do you say to their families about the choice you made?" asks Pelley.

"I honor their dead. ...Maybe they think that my presence dishonors their dead, but they made a choice the same as I made a choice, and my big problem is that, if they made that choice for anything other than they believed in it, then that's wrong," says Felushko. "The government has to be held responsible for those deaths, because they didn't give them an option."

Soldiers who want to be assigned to non-combat jobs have the option of applying for conscientious objector status.

Spc. Jeremy Hinzman, from Rapid City, S.D., filled out those forms, and while he waited for the decision on his request, he worked in a kitchen in Afghanistan.

The Army eventually told Hinzman he didn't qualify as a conscientious objector. "I was walking to the chow hall with my unit and we were yelling, 'Train to kill, kill we will,' over and over again," recalls Hinzman.

"I kind of snuck a peek around me and saw all my colleagues getting red in the face and hoarse yelling, and at that point, a light went off in my head and I said, 'You know, I made the wrong career decision.'"

Despite his decision to leave the army, Hinzman says he wasn't looking for a way out of his commitment to the military.

"I was told in basic training that, if I'm given an illegal or immoral order, it is my duty to disobey it, and I feel that invading and occupying Iraq is an illegal and immoral thing to do," says Hinzman.

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"Whether a country lives under freedom or tyranny or whatever else, that's the collective responsibility of the people of that country," says Hinzman.

He later adds that his contract with the military was "to defend the Constitution of the United States, not take part in offensive, preemptive wars."