why does romeo refuse to fight tybalt?

Romeo refuses to fight Tybalt because he has just secretly married Juliet, who is Tybalt's cousin. This marriage makes Tybalt Romeo's kinsman, creating a new familial bond. Therefore, Romeo's love for Juliet transforms his view of Tybalt from enemy to family, and he wants to maintain peace rather than continue the family feud by fighting Tybalt.