Why does Shakespeare create three sets of father-son parallel pairs in Hamlet?
Interesting question! Shakespeare used parallels to illustrate a theme in his plays quite often. In this case, the parallels give us contrasts (foils) to highlight the characteristics of each pair.
Polonius and Laertes demonstrate a father and son who care for each other, but Polonius is incredibly controlling over his children - he wants to make sure he has his fingers in their business at all times. Despite that, though, Laertes is ready to avenge his father's death at the hands of Hamlet when he comes back to Elsinore.
Hamlet and old Hamlet demonstrate a devoted son who misses his father deeply and desires to avenge his death, but lacks the ability to act until it is too late.
Fortinbras, whose father was killed by old Hamlet, serves as another foil to Hamlet in that he is a man of action, having initially engaged in hostilities against Denmark after his father's death, and finally being able to take the throne when all is lost within the Danish royal family.
Check the links below for more information on these characters and how they are similar and dissimilar. Good luck!