Or Shakespeare plagarized other plays and poems that he had access too.
He did take many of his plots from older plays. Romeo and Juliet (Giulietta e Romeo) was a popular Italian story. There were several versions of it. Shakespeare's play was based on the version by Matteo Bandello.
This was the common practice of the Middle Ages and early Renaissance. It was not considered plagiarism. An author took an existing story and refashioned it by adding what he considered the essential details of the story. Or he changed details of an Italian story to suite English practices and tastes.
A much earlier example is Chaucer's poem "Troilus and Criseyde". This is an ancient Greek tale, but Chaucer based his version on the poem "Filostrato" by the Italian Boccacio. It was just the way things were done.