The conflict between Tybalt and Mercutio is not personal. They fight because the Capulets and Montagues are fighting. The feud between the Montagues and the Capulets has been going on for a long time.In fact, it has been going on for so long that no one seems to know what started it.hen Mercutio and Tybalt get into a duel, they are fighting for honor. As soon as they meet each other on the street, they start insulting each other and it is not long before it turns into a duel, even though fighting has been forbidden by the prince. Tybalt is angry at Romeo.