Shakespeare never tells us why the families hate each other. It could be that the feud is so longstanding that the families themselves don't know why it started. The Montagues have always hated the Capulets and vice versa.
Some scholars see similarities between Romeo and Juliet and the story of Pyramus and Thisbe, who were also kept apart by feuding parents. Shakespeare uses the story of these lovers as the play being rehearsed by Bottom and his crew in A Midsummer Night's Dream.
Verona, Italy, where the play is set, was under the rule of Venice during Shakespeare's time. The city was known for its artists and architects; indeed, Verona has been called a "social, cultural, and economic fortress." Perhaps Mr. Montague and Mr. Capulet were rival builders or rival painters.
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