What is the reason Tybalt is looking for Romeo?
In act 1, scene 5, Romeo, Benvolio, and Mercutio attend Lord Capulet's ball disguised in masks like the other guests in attendance. When Romeo initially sees Juliet for the first time, he is overcome with emotion and gives a moving speech highlighting Juliet's physical attributes. Tybalt recognizes Romeo's voice and threatens to kill him:
This, by his voice, should be a Montague.— (to his PAGE) Fetch me my rapier, boy.—What, dares the slave Come hither, covered with an antic face, To fleer and scorn at our solemnity? Now, by the stock and honor of my kin, To strike him dead I hold it not a sin (Shakespeare, 1.5.52-58).
Tybalt is a Capulet, which means that he is sworn enemies with any member of the Montague family. Because Romeo is a Montague attending a Capulet party without invitation, Tybalt immediately takes offense and believes that Romeo is there to "fleer and scorn" their celebration. Fortunately, Lord Capulet intervenes and prevents Tybalt from attacking Romeo at the party. Later on, Tybalt searches the streets of Verona for Romeo and attempts to fight him for attending Lord Capulet's party.
In Act III, Scene 1 of Romeo and Juliet, Tybalt is looking for Romeo to fight him for attending the Capulet ball uninvited. Because the Capulets and Montagues are in a family feud, Romeo “crashing” the party is disrespectful and forbidden. When Tybalt sees Romeo on the street, he calls him out as being a “villain.” Little does Tybalt know that Romeo has already married Juliet, and they are now relatives. Because of this, Romeo doesn’t want to fight Tybalt, but he can’t tell him why. Mercutio, a hotheaded friend of Romeo’s, says he will fight Tybalt. They start to sword fight, and when Romeo attempts to break up the fight, Tybalt stabs Mercutio. Tybalt and his men run off, but come back still enraged at Romeo. Because Romeo has just lost his best friend, he fights and kills Tybalt. Now, Romeo has killed a relative by marriage and must flee Verona.
This scene is just another episode that seals Romeo and Juliet’s fate of bad luck keeping them from ever getting together.
Tybalt is looking for Romeo because he had challenged Romeo to a duel in revenge for Romeo’s appearing at the Capulet’s ball at the beginning of the play. This is the ball where Romeo meets Juliet.
In Act II, Scene 4, Tybalt is looking for Romeo as he wants to challenge him to a duel. Tybalt has vowed to seek revenge on Romeo for coming to a Capulet party without being invited.