Why do Tybalt and Benvolio fight?
In the first scene of the play, Sampson and Gregory (Capulets) encounter Abram and another servant of the house of Montague, and they begin a fight over whose master is better. Benvolio enters the scene, sees the fight, and he draws his sword in order to stop it. He says, "Part, fools! / Put up your swords. You know not what you do" (1.1.65-66). As the root of his name (bene) implies, Benvolio is good and peace-loving. He only draws his weapon in order to restore peace.
However, when Tybalt enters the scene and sees that Benvolio's weapon is out, he tells Benvolio to "Turn [...]; [and] look upon [his] death" (1.1.68). Benvolio insists that he only wants to "keep the peace" and encourages Tybalt to put away his own weapon or use it to help him to part the fighting men. Instead, Tybalt says he hates peace, the Montague family in general, and Benvolio specifically. He shouts, "Have at thee, coward!" and presumably lunges toward Benvolio, and so the two fight until they are broken apart by other club-wielding citizens. Essentially, then, Benvolio and Tybalt's fight is Tybalt's fault; he wanted to fight, and Benvolio did not.