The sad fact is that neither one of the two families knows or remembers why the feud began in the first place! This feud goes back before any of the people and characters within "Romeo and Juliet" were even born. They have all forgotten what they are fighting about.
The Montague and Capulet families have actually been feuding for years long before the generation that the story pertains to. The families could not live in Verona peacefully together,ever.
Shakespeare's lovers Romeo and Juliet belong to families which have been in opposition for generations, however not even the family patriarchs know the original basis for the feud.