Hate is explored in Romeo and Juliet through the concepts of tradition and revenge.
The Montagues and the Capulets have been fighting a feud for as long as anyone can remember. It is tradition to fight, and to hate one another. Tybalt is a perfect example of the fanatical hate embodied by the feud.
I hate the word(65)
As I hate hell, all Montagues, and thee.
Have at thee, coward! (Act 1, Scene 1, p. 12)
Why do the Montagues hate the Capulets? They hate each other because they have been raised to hate each other. Juliet bemoans the fact that she has to hate Montague, when Montague is not really a part of a man—it is only a name.
The second reason for hate is revenge. The feud causes killings, and killings create the need for revenge. This continues the feud. When Tybalt kills Mercutio, Romeo kills Tybalt. He does not even hate Tyablt, but he is in an impossible situation. Juliet even acknowledges this. She finds herself in an impossible situation: Her husband killed her cousin.
The prince tries hard to end the fighting by threatening to punish anyone who fights. He gives the heads of the two families a stern talking to, but it does not seem to help. He decides to make an example of Romeo, but all this does is lead to more fighting and death. It takes Romeo and Juliet's death to make everyone see the light.