Why do Sampson and Gregory fight with Montague's men?
At the very beginning of William Shakespeare's The Tragedy of Romeo and Juliet, Sampson and Gregory, two servants of the Capulet household, are carrying on a conversation about the possibility of meeting up with servants of the Montague household. The two households are the most powerful in Verona, Italy, and have carried on a family grudge for years. The quarrel between the two families is such a vicious one that lives have been lost because of it. Sampson and Gregory consider themselves members of the Capulet family due to their job positions and are extremely loyal to the people who are responsible for their well-being.
As Sampson and Gregory are "mouthing" and bragging about what sort of violent action they will take if they meet Montague men, they find themselves in exactly that situation. Abram and Balthasar, two of the Montague family's trust servants, meet them on the street. Sampson, who is the loudest and most daring of the two Capulet servants, decides to make a crude gesture at Balthasar and Abram.
...I will bite my thumb at them, which is disgrace to them if they bear it.
Of course, Abram and Balthasar and offended. Sampson and Gregory goad them into making the first move in violence, then the incident becomes a true swordfight. Tybalt, the bad-tempered and bloodthirsty cousin of Juliet Capulet, and Benvolio, the kind, peace-making cousin of Romeo Montague, each play a part in the resulting chaos.
In Shakespeare's Romeo and Juliet, the first line of the play, spoken by the chorus, establishes the situation Sampson and Gregory demonstrate in the opening scene you ask about. The play begins:
Two households both alike in dignity,
In fair Verona where we lay our scene
From ancient grudge, break to new mutiny,
Where civil blood makes civil hands unclean:...
The reason Sampson and Gregory want to fight Montagues is no good reason at all--an "ancient grudge." And recently it has flared into "new mutiny." The two Capulets are like almost everyone else in the play: full of blind hatred and bigotry and machismo.
In the opening scene, Gregory teases Sampson that he is slow to strike, and Samson replies that
A dog in the house of Montague moves me [to strike].
He not only implies that he is quick to anger by the presence of a Montague, but calls them dogs in the process.
The two then talk about not moving aside when walking by Montagues, then turn that into jokes about putting Montague maids against the wall, a sexual joke.
The two want to fight for the sake of fighting, and particularly for the sake of fighting Montagues. And, of course, for no good reason, that's what happens.
The only real reason that these two men have for fighting is the fact that they are servants of the Capulet family. The Capulets are, of course, enemies of the Montagues. They hate each other enough that even their servants fight.
Right at the beginning of the play, before they have met any of the Montagues, the two men are already ready to fight. Sampson, in particular, says bad things about the Montagues twice in the first 12 lines of the play.
Then Gregory says "The quarrel is between our masters and us their men." This means that the quarrel is between the houses, but it extends down as far as the servants.
These two fight so that the audience can see how deep this feud actually runs!
Can you imagine joining in a family feud...even if you were not part of either family? That's how these two are!
The fact that these characters are willing to join in the fray portrays how deeply the fray runs--it extends to servants and friends as well. Clearly the entire city of Verona has chosen a side!
They were fighting because they were servants of different households , the Monatugues and the Capulets . The Montague and the Capulet's are sworn enemies which of course would lead to the servants of these two households being enemies .
sampson and gregory fight with montague's men because they are sevants of the capulets and the two families hate each other so much it makes the survants hate the family too.