Does Romeo hate Tybalt, why?

There is no real evidence that would make us say that Romeo hates Tybalt personally as opposed to just hating the Capulets in general.

The two of them never actually speak to each other until the scene where Tybalt kills Mercutio and Romeo kills Tybalt.  In this scene (Act III, Scene 1) Romeo doesn't say anything angry to Tybalt when Tybalt appears.  Instead, he speaks soothingly to him.  This implies he doesn't hate Tybalt.  He does kill Tybalt, but in revenge for Malvolio.

So I don't see anything to imply that Romeo actually hates Tybalt.