Shooting oneself in order to be removed from the war was seen as an act of cowardice.
Most soldiers knew they could do that but out the sense of shame they avoided doing this. The shame of not serving in "The Things They Carried" and not participating in the war was one of the main motivators for many in the book. So when Kiley shoots himself in the leg, as they identify cowardice with death, threat it like he died. But somewhere they are jealous of him as he was able to take a bit of shame in order to leave the horrors of war.