I don't know if evil is the right term, but there are other words that are equally effective in describing Tybalt, such as vain, extremely rude, belligerent, aggressive, and quick-tempered and prideful. He acts before he thinks and he abhors the Montagues. All of these characteristics combine to make a character that is truly worthy of the loathing the audience feels for him, and it is due to this loathing that the audience is able to feel sympathy for Romeo’s character instead of Tybalt’s after Romeo kills him. Shakespeare, being the talented writer that he was, knew all to well how to gain the sympathy of audience for his protagonist, and this is perhaps the reason that he made Tybalt, perhaps not evil, but very easy to dislike a great deal.
Tybalt is not really an evil person. Tybalt's character just doesn't like the Montagues. Shakespeare makes Tybalt's character evil because each story has to have an antagonist to make the story interesting.
Tybalt isn't really evil. If he was, the whole Capulet family would be evil because they all have a hate toward the Montagues.
But Shakespeare makes him "evil" because every story needs or has a antagonist. Tybalt's character contradicts with Romeo's character which creates the story's ups and down.
Tybalt isn't really "evil". Look at things from his point of view for a moment. A Montague (his family's sworn enemy) has decided to trespass on a party he wasn't invited to. As a Capulet, he needs to protect his family's honor (big deal way back when). So he's gonna hate Romeo for a while. But then he kisses his cousin (Juliet) KISSES her! What gaul he has. Because of this, he decides to send a message to the Montague household, requesting that Romeo duels with him. Now Romeo, being the idiot he is, has been too busy getting married to Juliet to even think about going home so he never gets the message. But, Tybalt doesn't know that. All Tybalt knows is that Romeo is calling him cousin and using his family name, not something you would expect from a rival so he thinks he's making fun of him. So of course he's gonna get pissed.
Now with everything else not involving Romeo, he's not evil. He's just a remarkable swordsman and is a bit vain for it. He also is a bit short-tempered, but then most people in the Capulet family are. =P