Romeo's Punishment

In the book Romeo and Juliet by William Shakespeare I think Romeo's punishment is not fair. First of all, Tybalt killed Mercutio, thus enraging Romeo and making Romeo want vengeance so he killed Tybalt making it fair because one person from each house died so its even. The book describes "Alive, in triumph, and Mercutio slain. Away to heaven respective lenity, And fire-eyed fury be my conduct now! Now Tybalt, take the Villian back again that late thou gav'st me, for Mercutio's soul is but a little way above our heads, Staying for thine to keep him company. Either thou, or I, or both must go with him."(Act III, Scene 1, Line 120-125) This shows that Romeo is mad and wants vengeance for Tybalt killing his friend. Second, Its like an eye for an eye, therefore If Tybalt kills Mercutio than Tybalt has to die for it. Last, Romeo is only banished because Montague said to the prince "That's what you would have done.", making the Prince think that is an offense, he punishes Romeo for it. In conclusion, all these reason make up for why Romeo shouldn't be punished for what he has done to Tybalt.