Good question. Let's say that Romeo and Juliet are the personification of pure, true love. They basically fall in love at first sight, are madly in love with each other at the end of their first conversation, and are married shortly after. On top of those concrete events, their conversations are some of the most sappy love expositions ever written or spoken.
On to Tybalt. If Romeo/Juliet represent love, then Tybalt is the symbolic personification of hate. The guy is mad all of the time. Seriously. He wants to beat Romeo to a pulp for crashing the party. Capulet holds him off, but Tybalt simply decides to beat up Romeo at a later date.
Tybalt has his chance in Act 3, Scene 1. Tybalt is out looking for Romeo and finds him. Tybalt immediately challenges Romeo to a fight. Romeo's response is that he will not fight. Romeo's reason is that they are now related through marriage, but he doesn't tell Tybalt that. Tybalt is not about to be turned down. Romeo may be a lover not a fighter, but Tybalt is for sure a fighter not a lover. Swords are drawn, Mercutio is killed, Romeo is super mad, and Romeo kills Tybalt. From here forward, Romeo and Juliet's relationship is on a downward spiral until both of them are dead.