Prince Escalus discourages the fighting between the two families because he sees just how much damage it is causing the city of Verona and its citizens on the whole. As we see in the very first scene, when the Capulet and Montague households' servants break out into a fight on a street in Verona, after Benvolio tries to break up the fight and Tybalt joins in the fray, making things worse, what happens next is that all of the citizens present also join in on the fight, proclaiming:
Clubs, bills, partisans! Strike! beat them down! Down with the Capulets! Down with the Montagues! (I.i.68-70)
In addition, not only does their fighting cause this one whole-city riot, Prince Escalus points out that it has caused riots twice before, making this the third riot, as we see in his lines, "Three civil brawls, bred of an airy word ... / Have thrice disturbed the quiet of our streets" (85-87). Hence, since the two families' fighting is causing whole city riots, endangering citizens' lives, Prince Escalus wisely sees that their fighthing must come to an end.