In The Things They Carried, why do the soldiers lighten their burdens by making insensitive jokes about casualties?

Dehumanization is a common threat shared among military members across centuries of warfare.  It is lessening the human characteristics of the enemy through ridicule, denial, sarcasm and labels that tend to shift the focus away from human characteristics toward generic or non-human characteristics.  In essence, it is removing the human from humanity.  Although typically associated with warfare, dehumanization can be found in non-violent conversation and is generally part of racial epithets.

In The Things They Carried, each member of Alpha Company bears a burden of guilt and fear.  The deaths Alpha Company suffers weigh heavily upon the living.  Lemon's death was perhaps preventable.  Lavender's death happened during a moment of nostalgia by Lt Cross, who wonders later if his inattention contributed.  Kiowa's death in an unbelievably senseless manner forever alters the members of the company.  The fear of death and suffering the soldiers face each day wreaks havoc with their mental well being.  In order to offset the guilt and fear the group turns to dehumanizing the enemy.  This allows them to attach their feelings to a generic entity and thereby further avoid guilt by blaming an actual person.  In short, the members use jokes to defray the mental anguish they all suffer.

The act of dehumanization as a coping mechanism is long understood and acknowledged among the military.  Nazis referred to Jews as "rats", US service members labeled North Vietnamese as "Charlie", and others have been called "dogs" and "cockroaches".  These terms are designed to separate the speaker from the emotional consequences of killing another human.  Even in self-defense, taking another life is not an easy thing.  There will be scars.  Dehumanization helps to offset the emotional grief in a mental coping mechanism.

The simplest answer?  To survive.