Tybalt's hatred towards Romeo stems from the longstanding feud between their opposing families. Tybalt is Juliet's cousin and a proud Capulet while Romeo is a Montague. The Capulet and Montague families have be engaged in a longstanding feud, which has caused conflict throughout Verona. Tybalt is depicted as a hot-headed, vengeful individual, who displays his violent temper and hatred towards all Montagues in the opening scene of the play when he draws his sword on Benvolio, who is simply attempting to end the conflict.
In addition to the fact that Romeo is a much-hated Montague, Tybalt recognizes Romeo's voice during his uncle's ball and is greatly offended that Romeo would sneak into his uncle's home. Lord Capulet prevents Tybalt from confronting Romeo during the ball but Tybalt ends up challenging Romeo to a duel in act 3, scene 1. Tragically, Mercutio stands up for Romeo and Tybalt manages to kill him while Romeo is inbetween them. Following Mercutio's death, Romeo gets revenge by killing Tybalt, which leads to his exile. Overall, Tybalt hates Romeo because he is a Montague and a sworn enemy, who attended his uncle's ball without permission.