A third argument made is that Hamlet has an Oedipal complex about his mother. This psychological disorder determined by Sigmund Freud involves the unconscious desire of a son to kill his father and take his place as the object of his mother's love. According to Ernest Jones, critic, in his article, "The Psycho-Analytical Solution," Hamlet tarries in his seeking revenge on Claudius because he shares Claudius's guilt in desiring Gertrude. Therefore, his inaction is a result of his "tortured conscience" and his melancholy is caused by his "repressed feelings." Jones further maintains that driven by the "unconscious" part of his mind, Hamlet is painfully thrawted. And, his "indignation" at his father's murder is superceded by his "intensest horror" at his mother's incestual relation with Claudius.
That Hamlet may have the Oedipal complex is evidenced, critics say, in his soliloquy against Gertrude in Act I
....She married. O, most wicked speed, to post
With such dexterity to incestuous sheets! (1.2.155-156)
and, especially when he rails against her like a jealous lover in Act III:
...You cannot call it love, for at your age
The heyday in the blood is tame, it's humble....
What devil ws't
That thus hath cozened you at hoodman-blind?
Eyes without feeling, feeling without sight...
...O shame, where is thy blush?
If thou canst mutine in a matron's bones,
To flaming youth let virtue bea as wax
And melt in her own fire. Proclaim no shame
When the compulsive ardor gives the charge (3.4.69-87)
The site below contains the full article on Hamlet's Oedipal Complex.
The most obvious and most talked about is that of the incestuous relationship between Claudius and Gertrude, not necessarily incest in the manner of blood relations getting together, but certainly marrying your brother's wife smacks of incest to Hamlet Jr.!
A second could be the somewhat historical context of the time which would certainly have influenced Polonius in thinking that Hamlet couldn't be serious in his affections for Ophelia given the tendency to keep things within the family or at the very least within royalty when it came to folks like the crown prince of Denmark. It simply wouldn't have been possible for Hamlet to be serious about Ophelia, something Polonius tells her about at length. But incest was relatively common in royal families at the time, why not here as well!