The soldiers in The Things They Carried talk a lot about courage, but mostly as an antidote to physical and moral weakness. Characters obsess about weakness. Not going to the war when drafted is seen as weak, but so is going to the war when your entire moral system is telling you to run away to Canada. No matter how strong and courageous you think the soldiers are, it never seems as if they'll be courageous enough; weakness will always prevail. And yet, the characters continue to blame themselves for it.
When the soldiers in The Things They Carried speak of courage, they're really referring to its opposite, weakness. All their strength is a reaction against the fear of weakness.
The true cowardice in The Things They Carried is not the fear of death or pain, as the soldiers believe it to be. It's the fear of cowardice itself, which drives men to perform acts that their consciences wouldn't otherwise allow.