Why do you think Shakespeare included two different perspectives of the cock crowing in Act I, Scene 1 of Hamlet — Horatio’s Pagan perspective...

Old King Hamlet's ghost's origins are questionable. He claims that he is in Purgatory, purging his soul of the sins with which he died when Claudius struck him down without giving him opportunity to make confession and atone. He says he is "confined to fast in fires / Till the foul crimes done in [his] days of nature / Are burnt and purged away" (1.5.16-18). The problem? Catholics are the only Christians who believe in Purgatory; however, Hamlet attends school in Wittenberg, a city famous for being the origin of the Protestant Reformation. Protestants do not believe in Purgatory. So, is Catholicism or Protestantism ruling here? If it is Catholicism, then the ghost can legitimately be Hamlet's father, returned to charge his son with exacting revenge on his murderer. If it is Protestantism, then the ghost cannot be Hamlet's father, and this is why Horatio (Hamlet's university friend) fears the ghost might be a demon sent to "deprive [Hamlet of his] sovereignty of reason / And draw [him] into madness" (1.4.81-82). If the ghost is really a demon, then it poses a serious danger to Hamlet. This ambiguity is later indirectly answered by the fact that the ghost that visited Hamlet was speaking truthfully: his brother did murder him in the way that he described.

So, the dual accounts concerning the rooster's crow that prompted the ghost's original disappearance points to the confusion that will surround it later, when Hamlet is present and can speak to it. Horatio gives it a pagan origin; Marcellus, a Christian one. This indirection foreshadows and underwrites the similar indirection concerning Hamlet's father's ghost.