Shakespeare's plays start in the middle of things (as all great stories do). We, as the audience, are entering a story that's already in the midst of its narration. In the Prologue, we learn that "from ancient grudge break to new mutiny" (line 3). The feud is old but the fighting has recently broken out again. We don't know why. The Prologue also sets up the fact that these are two families that are incredibly similar. They both reside in Verona. They are wealthy and established families -- "both alike in dignity" even. For all practical purposes, they should be allies rather than enemies.
The next hint that we get comes from the Prince in Act 1 Scene 1. The Prince, after breaking up the fight in Act 1 Scene 1, states: "And hear the sentence of your moved prince./Three civil brawls, bred of an airy word." Very recently, three different public fights have broken out amongst the Capulets and Montagues. The feud between the two families has become public and violent enough for the Prince to worry about the safety of his people and his city.
I would argue that's part of the tragedy: We don't know why they are fighting, thus we can't fully understand what would be at the very root of why Romeo and Juliet can't be together. Shakespeare sets the play in the heat of Verona, Italy. The days are long and hot, thus mirroring the moods of the citizens. They are physically hot and they are hot with anger -- little things can set them off. More than anything, Shakespeare is showing a harsh light on humanity: Humans hold grudges. We hold prejudices and hate in our hearts that sometimes can't even be explained by ourselves. The tragedy of Romeo and Juliet is that it doesn't have to end in tragedy, but it does.