Why does Montresor feel he has the right to take justice into his own hands?
This is an interesting question. Evidently Monrtresor does not care about the moral or legal right to kill Fortunato and does not even consider it "justice" to do so. He knows that what he intends to do is a criminal offense and that if he were caught he would be sentenced to death. He has no legal defense. He knows he is committing a crime and he doesn't care. He only cares about satisfying his desire for revenge and about not getting caught. In this respect he is no different from the narrator of Poe's story "The Tell-Tale Heart." That person too was aware that he was committing a crime and that it was a capital offense.
Even if Montresor were on trial for murder and recited the "thousand injuries" he had suffered at the hands of Fortunato, the horrible way in which he had killed him would have been sufficient to get him the death penalty. The entire story is about the careful way in which he managed to elude "justice." After all, if a man is going to commit a cold-blooded, premeditated murder, how can we expect him to be concerned about such a thing as "justice"? People commit murders all the time without worrying about justice, except in the sense that the agents of justice might find them out. The world is full of people like Montresor. He is a far cry from Dostoevsky's Rodion Raskalnikov, who committed a double murder in Crime and Punishment and was so tormented by guilt that he gave himself away and was sent to Siberia.