Since you have not indicated which act this scene 1 is in, let me answer the question for Act III, scene 1 rather than Act I, scene 1 so that you may have whichever response you need.
In Act III, scene 1, of "Romeo and Juliet," the climactic fight scene is brought on first by the exceptionally hot weather which has irritated Mercution and brought on his ire. [That his temperament would become more choleric is in correspondence to the beliefs of the Romans who thought that one's personality was caused by certain "tempers" in the blood.] To Benvolio's advice that they should retire because "For now these hot days is the mad blood stirring"(III,i,4) by retorting,
Thou art like one of those fellows that when he enters the confines of a tavern, claps me his sword upon the table and says,'God send me no need of thee!' and by the operation of the second cup draws it on the drawer, when indeed there is no need (III,i,5-8)
Mercutio continues by accusing Benvolio of transferring his hot temper--"hot a Jack in thy mood as any in Italy"(III,i,9)--to him. As they quarrel, the Capulets appear; Mercutio then banters with the hot-headed Tybalt, who has accused him of consorting with Romeo. Mercutio begins by using a pun on the word "consort," but soon the dialogue accelerates as Mercutio declares, "I will not budge for no man's pleasure, I" (III,i,42).
Then, when Romeo arrives, Tybalt displays hostility,saying to Romeo,
Romeo, the hate I bear thee can afford/No better term than this--thou art villain. (III,i,49-50)
When Romeo, who has already married Juliet and is now a kinsman to Tybalt--unbenowst to Mercutio--replies, deferently to Tybalt,
Tyubalt, the reason that I have to love thee/Doth much excuse the appertaining rage/To such a greeting. Villain I am none,/Therefore farewell. I see thou know'st me not (III,i,50-53)
This response absolutely enrages the already testy Mercutio and he draws his sword against Tybalt accusing Romeo of "calm, dishonorable, vile submission!" (III,i,61).
Thus, the fight is brought about as it becomes one of defense of the honor of the Montagues initiated by the hot, irritating temperatures of the day, Tybalt's insults, and Romeo's attempt to ameliorate the hostilities which Mercutio perceives as weakness.
The cause of the quarrelling and fighting in the very first scene is reflective of the deep level of anger and "blood feud" that exists between the Capulets and Montagues. It is evident from the opening that these two families consider themselves arch enemies, antagonists to one another, and that this relationship predicated on intense dislike has been present for ages. The notion of "blood feud" is a good way to describe it and, like most levels of hatred, it has been passed down from generation to generation. There does not need to be a specific reason or person for the fight to start.
When the audience first sees him, Lord Capulet is calling for a sword to join in the fighting of the servants and young men in the opposing households. This would indicate to us that he is the aggressor, but it is also revealed that the intense nature of the dislike between both households causes different people to be initators of conflict, if nothing else as reacting to what someone else did in the past.