In the very first scene of the play, while Gregory was taunting at first and resistant to fighting, as soon as he sees Tybalt entering the public place from a distance, he incites Sampson to fight because he knows that if a swordsman like Tybalt is in the fray, they cannot lose.
This scene opens with Gregory and Sampson, servants of Lord Capulet, walking through some public place of Verona, possibly a town square, or piazza. As they walk, Sampson tries to prove his aggressiveness by insisting that if they should happen to run into any Montagues, he will not hesitate to draw his sword. However, Gregory insults him by insisting that he is really a coward. Gregory even seems to be more resistant to fighting than Sampson by reminding Sampson of the legal consequences of fighting. For example, Gregory reminds Sampson of the legal consequences when Sampson declares that if "[they] be in choler, [they'll] draw," meaning that if he and Gregory are angered by the Montagues, he and Gregory will draw their swords. Gregory reminds Sampson of the legal consequences when he responds to Sampson's comment by making a pun of the word "choler" and turning it into "collar," referring to a hangman's noose, thereby reminding Sampson that if he does draw his sword, he will most likely be hung: "Ay, while you live, draw your neck out of the collar" (I.i.3-4). When Gregory and Sampson do see two servants of Lord Montague's, even though Gregory commands Sampson to draw his sword, Gregory still shows more resistance to fight than Sampson does. When Sampson comes up with the idea to make the Montagues instigate the fight by insulting them, Gregory thinks of the more subtle approach to frown at the two servants as they pass by. It's Sampson who thinks of the far more aggressive, more insulting approach of biting his thumb at the Montagues, a sign of insult and "contempt" (eNotes).
It's only when Gregory sees Tybalt that Gregory starts seriously encouraging the fight. As soon as he sees Tybalt, he tells Sampson to say to Abram, one of Lord Montague's men, that Sampson is a better fighter than Abram, as we see in Gregory's lines to Sampson, "Say 'better.' Here comes one of my master's kinsmen" (53-54). The reason why Gregory incites Sampson to provoke Abram is because Gregory knows that Tybalt is a champion fighter, and if he is with them, the three Capulets absolutely cannot lose the fight to the Capulets.