This scene, of course, establishes the conflict between the Capulets and Montagues, and introduces us to Tybalt, whose violent temper creates an immediate threat to Romeo:
Fetch me my rapier, boy. What dares the slave [Romeo]/ Come hither, cover'd with an antic face,/ To fleer and scorn at our solemnity?
Tybalt incorrectly assumes that Romeo is trying to join the Capulets' party in order to ruin the celebration, and we know that Romeo's motivation is to get as close to Juliet as possible. Given Tybalt's temper and his threat to Romeo, however, Capulet realizes a disaster is about to ruin his celebration.
Capulet's response to Tybalt's threat is to point out that Romeo
. . . bears him like a portly gentleman;/ And, to say the truth, Verona brags of him/ To be a virtuous and well-govern'd youth; I would not for the wealth of the town/ Here in my house do him disparagement.
As the host of the celebration, particularly one taking place in his home, Capulet's first duty is to insure his guests' safety and comfort and, second, he reminds Tybalt that Romeo has a good reputation in the town--"a virtuous and well-govern'd youth." It would make no sense, then, for someone in Capulet's family to attack a young man of good reputation, who is also, as a guest, under Capulet's protection.
Unfortunately for the Capulets and Montagues, Tybalt, whose temper is his controlling feature, agrees to leave Romeo alone but says
I will withdraw: but this intrusion shall/ Now seeming sweet convert to bitter gall.
In other words, even though Romeo's attendance at the celebration will not be punished, Tybalt clearly intends to attack him when he is no longer a guest in Capulet's home and under his protection. Almost any time a Shakespeare character says something like "I will withdraw," that usually means he'll be back with a vengeance.
In Act I Scene 5 of William Shakespeare's Romeo and Juliet, Lord Capulet gives two reasons for preventing Tybalt from attacking Romeo. First, he says:
Content thee, gentle coz, let him alone.
He bears him like a portly gentleman,
And, to say truth, Verona brags of him(70)
To be a virtuous and well-govern'd youth.
His argument in this passage is that Romeo is behaving properly and has a general reputation of being an honourable and well-behaved young man. Given that Romeo has done nothing disruptive and that there is no good reason to suspect he will, there is no reason to attack him.
When Tybalt persists in making threats, Capulet points out that this is insubordinate, and that he should obey the orders of the head of the household, asking rhetorically "Am I the master here or you?"