In Act 5, why does Hamlet insist that Horatio remain alive? What must Horatio do for Denmark?
Hamlet implores Horatio, "Report me and my cause aright" because he wants everyone to know the truth about recent events. In a number of Shakespeare's plays, such as Romeo and Juliet, a character such as Horatio must survive in order to inform the person who will re-establish civil order---in this play, it's Fortinbras---about the turmoil that led up to the tragedy. For Denmark, then, Horatio must explain what has happened to Fortinbras so that he can re-establish order.
Although Horatio wants to die with his friend, Hamlet insists that he "tell my story." Twice Hamlet has explained the reason Horatio must not drink any remnant of the poison. Horatio is the only character still alive who knows the entire story of King Hamlet's murder and Hamlet's plan to seek revenge. Furthermore, Hamlet endorses Fortinbras as the next king so it is logical that Horatio share the details with him.
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