The stare down is primarily for others. It lets each woman pretend she is the "lady" and that it is the other one who is crude and wants to fight. Also, it shows others who are watching that she is unafraid of the other woman. The secondary purpose is to intimidate the opponent. If either backs down during the stare down, she in effect has lost the fight. The stare down continues until others pull them away, until one backs down, or until a fight begins.