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The reason why John doesn't give Romeo the letter
The health inspector suspected that John might have plague. So Romeo locked John in a house and he was unable to leave. The letter was really important and if Romeo didn't know Juliet was faking her death it'd cause lots of problems. -
John had small conversation with Laurence at first
John and Laurence are both priest and Romeo's messenger. Laurence asked if Romeo have a letter for me ?This is a reply to his letter, warning him that Juliet is planning to fake her own death, and John said he never actually gave Romeo your letter.