Romeo does not want to fight Tybalt because he is Romeo's wife's cousin. But Tybalt does not know this, and neither does anyone else except Juliet, the Nurse and the Friar.
Tybalt thought that romeo was faking and trying to trick him. Tybalt continued to try and get romeo to fight him but romeo just could not due to the fact that Tybalt was now romeos cousin or brother because of his love to Juliet.
Only Juliet knows about Romeo's motive not to fight Tybalt, as he confides in her about his love for Tybalt being fueled by their sudden family connection through marriage. Juliet is the only one privy to this information in the play.
Tybalt wants to fight Romeo... :)
Romeo kills Tybalt.
earlier in the play, romeo crashed a Capulet party. angry, Tybalt swore revenge with a sword fight. Romeo's friend mercutio ends up fighting Tybalt, and romeo attempts to intervene by stepping between them. Tybalt stabs mercutio, despite Romeos attempts to end the fight, and mercutio dies. Romeo and Tybalt then fight, and romeo kills Tybalt, and romeo is banished from Vienna. Merutio, romeo and Tybalt sword fight.
At first, Romeo does not want to fight with Tybalt because he is now married to his kinswoman, Juliet. This makes Romeo and Tybalt of the same family, and Romeo does not want to fight his own.
Tybalt was asking for a fight with Romeo. Since he was married to Juliet and Tybalt was now his cousin, he refused to fight him. Then Mercutio asked to fight Tybalt and in a way kind of tempted him to fighting. Tybalt ended up killing Mercutio because Romeo got in the way when trying to stop the fight between the two. So now Romeo is angry that his friend Mercutio is dead and Tybalt doesn't have a scratch. So, Tybalt and Romeo fight and Romeo kills Tybalt.
Romeo finally fought Tybalt because Tybalt killed Mercutio.
Romeo picks a fight with Tybalt in Shakespeare's play "Romeo and Juliet" after Tybalt insults him and his friends at a party. Tybalt challenges Romeo to a duel, but Romeo refuses to fight. This leads to Mercutio, Romeo's friend, stepping in and fighting Tybalt instead, resulting in tragic consequences.
Tybalt wants to fight him. Tybalt always wants to fight someone, and he has fastened on Romeo after Tybalt spotted him at the party in Act I Scene 5.
Mercutio is the one who decides to fight Tybalt.