Benvolio suggests leaving because they might otherwise get caught up in a brawl with the Capulets. Mercutio then points out that Benvolio himself is the kind of man who could start a fight anywhere and with anyone. Benvolio replies that Mercutio is even worse than he is.
At that point the Capulets do, indeed, appear and Benvolio becomes concerned. Mercutio, however, says, "I care not."
So, though he may not actively want to confront them, he is certainly not going to run away now they are here.
It is precisely because of this stubbornness that Mercutio initially refuses to leave.