Romeo calls himself fortune's fool because he feels a greater force, like fate, is working against him, especially after Mercutio's dying words of a plague on both houses involved in the play. Romeo is forced into a vicious circle of death and murder that will keep the two houses in the play from ever mending their differences.
After Mercutio's death, Romeo kills Tybalt, who was Mercutio's killer, despite having initially no desire to fight the man. The death of Tybalt stains Romeo's reputation, gets him banished and sets the groundwork for the rest of the play. Romeo feels strongly that fate, fortune or chance is moving against him and Juliet, no matter what he does.