Tybalt is offended that Romeo dared to show up at the Capulets' party, and so he goes in search of Romeo the next day in order to challenge him to a sword fight. For Tybalt, it is a matter of family honor. Additionally, Tybalt is also prone to violence and likes a fight (he said earlier that he hates peace).

Romeo is at his wedding with Juliet when Tybalt approaches Mercutio and Benvolio looking for him. Mercutio eggs Tybalt on, telling him to couple his "word" with a "blow," or a physical strike at one of them. Tybalt declares that he is quite ready to fight if Mercutio gives him a reason to do so, but Mercutio claps back, asking if Tybalt cannot find a reason on his own—with the implication being either that Tybalt is not very smart or not very courageous.

When Mercutio asks, "Could you not take some occasion without giving?" he is taunting Tybalt, daring Tybalt to fight, which Tybalt is certainly willing to do.

In this scene, Tybalt insults Romeo and Romeo ignores him because he is so happy, since he just came from his wedding. Tybalt then says he would like a word with one of them, Mercutio and/or Benevolio.  Mercutio dares Tybalt to add a blow to whatever he has to say and Tybalt says if he gives him reason to he will.  That is when Mercutio says, "Could you not take some occasion without giving?"  I think Mercutio says do you always have to raise your sword instead of just talking.  Why does there always have to be a duel?  Why can't it just be "friendly" talk? Tybalt continues to incite and insult Mercutio and the duel ensues leaving Mercutio dead and Romeo defending his honor.