In the play, Hamlet, why is our lead character so critical of women?

Hamlet's critical attitude towards women stems from the disgust that he feels for his mother. He feels betrayed by her and believes that she was complicit in his father's heinous murder. By marrying his uncle, Claudius, and denying him access to the throne, Hamlet is of the contention that she has denied him his birthright and has committed an immoral act, incest. Furthermore, Lady Gertrude is constantly at Claudius' side, supporting him in his criticism of Hamlet. Hamlet deeply resents his mother for all the wrongs he feels she has done to him.

When Hamlet converses with his father's ghost, it requests that he does not turn against his mother:

... nor let thy soul contrive
Against thy mother aught: leave her to heaven
And to those thorns that in her bosom lodge,
To prick and sting her.

The ghost asks Hamlet not to judge her and leave it to heaven. She must be punished by her own conscience and guilt and endure its torment. In spite of this, Hamlet turns against her and confronts her in her chamber later in the play (Act 3, scene 4). He is quite rude and insulting, almost threatening, causing her to fear for her life and cry out:

HAMLET: Now, mother, what's the matter?

QUEEN GERTRUDE: Hamlet, thou hast thy father much offended.

HAMLET: Mother, you have my father much offended.

QUEEN GERTRUDE: Come, come, you answer with an idle tongue.

HAMLET: Go, go, you question with a wicked tongue.

QUEEN GERTRUDE: Why, how now, Hamlet!

HAMLET: What's the matter now?

QUEEN GERTRUDE: Have you forgot me?

HAMLET: No, by the rood, not so:
You are the queen, your husband's brother's wife;
And--would it were not so!--you are my mother.

QUEEN GERTRUDE: Nay, then, I'll set those to you that can speak.

HAMLET: Come, come, and sit you down; you shall not budge;You go not till I set you up a glass
Where you may see the inmost part of you.

QUEEN GERTRUDE: What wilt thou do?
thou wilt not murder me?
Help, help, ho!

In the wordplay between the two, Gertrude tells him that he has offended his father, Claudius, by presenting a play about a king's murder. Hamlet responds by saying that she has offended his father, King Hamlet, by having done what she did. When she reprimands him, he tells her that her tongue is wicked. She is shocked by this rude response and asks Hamlet whether he has forgotten to respect her. Her son swears on the cross that he has not, but expresses regret that she is his mother.

When Gertrude realizes that she cannot reason with Hamlet, she offers to have others talk to him. He then tells her that she will not budge for he intends to hold up a mirror so that she may see inside herself. Gertrude is anxious and fears that Hamlet will kill her. She cries out in distress.

This misogynistic display by Hamlet is transferred to Ophelia, Polonius' daughter. He confuses her by expressing his love, desire and affection for her at times and then rejecting her outright at others. This might also be part of his plot to make others believe that he has lost his mind. In one of their conversations he tells Ophelia:

I have heard of your paintings too, well enough; God
has given you one face, and you make yourselves
another: you jig, you amble, and you lisp, and
nick-name God's creatures, and make your wantonness
your ignorance. Go to, I'll no more on't; it hath
made me mad. I say, we will have no more marriages:
those that are married already, all but one, shall
live; the rest shall keep as they are. To a
nunnery, go.

He says that women are deceptive and they hide their true intentions, presenting themselves differently to their true nature. Women use their wiles to mislead and are flirtatious. He tells her that he has had enough of that, alluding to his mother, since it has angered him. He also tells her that there will be no more marriages, suggesting that he won't wed Ophelia. Only one marriage will not survive (the one between his mother and Claudius) and the rest will continue as they are. He tells Ophelia to become a nun where she would certainly have to make a vow of chastity.

Later, when they watch the play, he makes a number of saucy and suggestive remarks to Ophelia and asks if he could rest his head in her lap. It is this kind of behaviour which utterly confuses the poor girl and is partly the reason for her eventual suicide.