At the beginning of Act III, Scene 1, why does Benvolio think there will be a fight?
At the beginning of Act III, Scene 1, Benvolio thinks there will be a fight because it is a hot day. He thinks hot days lead to "mad blood stirring."
Essentially, Benvolio worries the hot day will make people ill-tempered and prone to engage in conflict. He tells Mercutio they should both go indoors to avoid running into any Capulet men. His fear is that, if they do run into any Capulets, a brawl would be very likely, considering the extreme heat of the day. Benvolio equates the sun's heat to the tempers of hot-blooded young men.
For his part, Mercutio contends that Benvolio is as hot-tempered as any young man in Italy and that he's more prone to anger than even he would admit. He mentions Benvolio has picked fights before, and basically chastises Benvolio for being hypocritical in this regard. Mercutio maintains that Benvolio's "head is as full of quarrels as an egg is full of meat" and that he's even quarreled with a man whose coughing woke up his dog.
Mercutio accuses Benvolio of falling out with his tailor "for wearing his new doublet before Easter," and he also mentions the time Benvolio quarreled with someone for "tying his new shoes with old ribbon." In citing these examples, Mercutio contends that Benvolio has no right to accuse him of a hot temper when he's just as guilty of it himself.