"Content thee gentle coz, let him alone."
In Act I Scene 5 Tybalt tells Capulet that Romeo, a Montague, has crashed the party. Capulet tells Tybalt not to bother about it: Romeo has a good reputation, and is behaving himself, so why disturb the party at which everyone is having a great time?
Nobody sent Tybalt. Tybalt sent Tybalt. Why? Because he's decided he doesn't like Romeo and Capulet stopped him from fighting at the Capulet party in Act 1 Scene 5. Tybalt has decided to take matters into his own hands by issuing the challenge.
Romeo and Juliet meet and fall head over heels in love with each other. Tybalt recognizes Romeo and starts to confront him; instead, Lord Capulet restrains Tybalt.
Tybalt becomes upset when he recognizes Romeo at the Capulet party, as he sees it as a direct challenge to his family's honor. Capulet responds by scolding Tybalt for causing a scene and tells him to calm down and let Romeo enjoy the party, not wanting any disruption to the event.
In Act 1. Scene 5 Romeo and his friends have gatecrashed Old Capulet's party (it was an open invitation, so gatecrashers were expected). Tybalt realises that Romeo - a Montague - is present, and wants to start a fight. Old Capulet says: 'Chill, man, it's a party, heyyy'. But Tybalt wants to start a fight anyway. The actor playing Tybalt has to find some way to show us why Tybalt would rather fight Romeo than chill at a party. There are various ways to do this, it depends on the actor.
These words were spoken by Lord Capulet in Act 3, Scene 1 of Romeo and Juliet. Lord Capulet is appealing to Prince Escalus for justice after Tybalt is killed by Romeo. He insists that Romeo must pay for his crime with his life.
Tybalt sends for his rapier, a kind of sword, in Act I Scene 5 so he can have a fight with Romeo. Capulet forbids it, fortunately.
Tybalt recognizes Romeo's voice at the Capulet's feast and is outraged that he has crashed the party. He informs Lord Capulet about Romeo's presence and insists that he should be removed from the party immediately. Lord Capulet, however, allows Romeo to stay because he does not want to cause a scene at the feast.
In this scene Tybalt seeks Romeo because he is mad at Romeo for being at the party at the Capulet house, and wants revenge. In the play, this is the only reason but in the movie, Tybalt is mad at Romeo because he knows Juliet is falling for him.
The Capulet's ball was to take place at night
In Act I, Scene V of Romeo and Juliet, Romeo and his friends crash the Capulet ball. Romeo meets Juliet and they fall in love at first sight. Tybalt recognizes Romeo and wants to fight him, but Lord Capulet stops him, not wanting trouble at the ball.
Capulet allows Romeo to stay at the party because Tybalt does not recognize him as a Montague. In addition, Capulet does not want to create a scene at the party by causing a confrontation with a guest, so he chooses to let Romeo stay and enjoy the festivities.