Why does Hamlet recall the story of Priam and Pyrrhus in Act 2 of Shakespeare's Hamlet?
Does it reflect it any way upon Hamlet's own situation?
To understand Priam and Pyrrhus in Hamlet, we first have to identify the two men who are mentioned in the allusion.
The characters are from the stories of the Trojan War. For this allusion to be effective, most of the Elizabethan audience the play was performed for would have known of the story. Priam is killed by Achilles' son Neoptolemus (also known as Pyrrhus).
It is possible that Hamlet is comparing Pyrrhus to his uncle, Claudius. Some sources record the presence of Piram's wife, Hecuba, who helplessly stands by watching the murder. Hamlet wonders if perhaps Gertrude stood by and watched while Claudius murdered King Hamlet. By doing so, Gertrude might knowingly have aided Claudius in the murder. But this idea is swept aside when the ghost of Old Hamlet speaks to his son while Gertrude (not seeing the ghost) watches. The ghost confirms that murder was not her sin. Instead, the ghost tells Hamlet that judgement for the crime she has committed—marrying her brother-in-law (seen as incest by the Elizabethans)—should be left to heaven.
The comparison that Hamlet makes seems clear enough. It is, however, ironic and provides an instance of sad foreshadowing (of which Shakespeare most certainly would have noticed and used intentionally) that Priam also kills Pyrrhus' son. By the end of the story, through conniving treachery, Hamlet has been poisoned by Claudius and dies.
In terms of the choice of Priam and Pyrrhus, Hamlet is drawing a parallel between the murder of Priam by Pyrrhus, and the murder of his father, Old Hamlet, at the hands of Claudius, who then "steals his throne and wife."
Ultimately, it is impossible to be exactly sure how Shakespeare intended to use his reference to Priam and Pyrrhus, but it is clear that he is drawing attention to the idea of one man killing another.
What if Hamlet is Pyrrhus and Claudius is Priam? That might make sense, since Pyrrhus was a good guy and needed to take revenge on Priam (the evil Trojan king.) By referencing the relationship between Pyrrhus and Priam, Hamlet might be foreshadowing his own killing of Claudius.
I am saying perhaps this is Hamlet thinking ahead about getting revenge for his father's death. Just thinking out loud; I'm studying this too. :)
It does reflect on his situation. Pyrrhus is the ultimate avenger, who delays only briefly before the grisly business of mincing King Priam. Hamlet fails to see his situation in Pyrrhus' delay or see that Pyrrhus is resolved to see its bloody execution fulfilled. He is waiting for the part where Queen Hecuba cries over her mangled husband. (For all we know an emotion particularly absent from Queen Gertrude.) Hamlet is testing the First Player's ability to strike emotion in the soul of an observer and evoke a reaction that is seen as guilt.
The other interesting thing he fails to pick up on is that he misremembers the opening lines. It is somehow stuck in Hamlet's mind that Pyrrhus is like the Hyrcanian beast, though the words are nowhere in the play. The revenge by Pyrrhus does not make him an admirable individual. King Priam is remembered through the play as the one to be admired. Avengers are beastly. There is no nobility found in Pyrrhus' action. History holds a special place for people like King Priam, Julius Ceasar and Alexander the Great not Pyrrhus. Prince Fortinbras learned from his uncle that revenge is not the noble path of princes.
Hamlet strikes down the unseen good old man (Polonius) and sets himself on a collision course with Laertes that results in both their deaths.