The conversation between Sampson and Gregory, two servants of the house of Capulet, make it clear that they are out to provoke the Montagues, their masters' lifelong enemies, into a fight. They speak about how much they hate the Montagues and how they would fight them in an encounter. When they see two Montagues, Abraham and Balthasar, approaching, they decide to start a quarrel:
I will frown as I pass by, and let them take it as
Nay, as they dare. I will bite my thumb at them;
which is a disgrace to them, if they bear it.
Sampson is clearly intent on daring the two men and decides to make an insulting gesture which, he knows, would offend the two and draw them into a confrontation. He bites his thumb, which is a vulgar indication of his disrespect for the two men. Abraham questions his action and Sampson at first denies the gesture but then states that he is, after all, biting his thumb. Gregory then asks Abraham if he is quarreling, an accusation that he denies.
Sampson, for his part, informs Abraham that he is for him, since he is employed by a master similar in status to his. He will, therefore, not stand back and tolerate any abuse. Abraham's response, "no better," is a clear insult (he claims that his master is better than theirs or that they are equal in status). The two Capulet servants then insist that he acknowledge the superiority of the house they serve, and when he refuses and tells them that they are lying, Sampson then challenges them to a duel:
Draw, if you be men. Gregory, remember thy swashing blow.
Sampson has probably just noticed Tybalt, also of the Capulet house, on his way, and is obviously emboldened. The men start fighting and Benvolio (a Montague) steps in and attempts to stop the fight. Tybalt then arrives and threatens him. The fight soon spreads and a number of supporters from both houses join in the fray, including lords Montague and Capulet.
It should be obvious that the chief perpetrator in this incident is Sampson. He took the lead throughout and was intent on creating a fracas, continuously confirming with Gregory whether they would have the law on their side and then succeeding in his nefarious purpose.