why do the boys fight?

The boys fight because in their "society," aggression is
the answer.  The story is set in a time well before peer counseling and mediation.  It
is also set in a time when children were not given credence or validation as they are
today.  Without the proper "skills," such as peer counseling and mediation, youngsters
sometimes reacted with gut reactions, hence, physical aggression.  In addition, poverty
contributes to aggression.  Although I do not think that poverty is the issue in The
Outsiders.  The wealthy kids in the community were physically aggressive as
well!

So, in a nutshell, the times lent themselves to
aggression.  The United States was in the middle of a war.  The president had recently
been assassinated.  Cuba was a threat to the United States.  The nation was deeply
divided.  I think kids feel helpless in times of political strife as in "What can we
do?" and fighting may serve as an outlet for their frustrations.