Why there was a strain between the families of Romeo and Juliet?

The very first mention of this feud is in the play's Prologue.  The speaker refers to both families, the Capulets and the Montagues, as "alike in dignity" (line 1); thus they are of the same class and social standing.  Further, they bear toward one another an "ancient grudge" that, during the course of the play, will result in "new mutiny" (3).  The cause of their long-standing feud is never revealed to the audience; however, we...

The very first mention of this feud is in the play's Prologue.  The speaker refers to both families, the Capulets and the Montagues, as "alike in dignity" (line 1); thus they are of the same class and social standing.  Further, they bear toward one another an "ancient grudge" that, during the course of the play, will result in "new mutiny" (3).  The cause of their long-standing feud is never revealed to the audience; however, we see the new examples of insults the families trade in the play.  In fact, the very first scene presents such a conflict when Sampson and Gregory, of the house of Capulet, end up engaging in a street fight with two servants of the house of Montague when Sampson asserts that his master is "better" than theirs (1.1.61).  Further, when Romeo and his friends go to the party at the Capulets' house, Tybalt takes it as a terrible insult and wants to fight Romeo the next day.  When Romeo refuses to fight, Romeo's friend, Mercutio, fights Tybalt instead, believing that Romeo dishonors himself by resisting.  When Tybalt kills Mercutio, Romeo kills Tybalt, increasing the tensions between the houses even more.

It is possible that, since both families are so well off, that the patriarchs fought over land or property or something of that effect.  Perhaps they wounded each other's pride a long time ago and have never dropped the grudges they held.  We simply don't know for sure because it is never stated in the play.