Hamlet is upset about his mother's marriage for two reasons. First, she remarried incredibly quickly after his father's sudden death. This makes it seem as though she did not love him with any degree of constancy; her love must have been slight, indeed, to forget it so soon after her husband's death. Second, Hamlet is upset because she married his uncle, his father's brother, and Hamlet feels that his father was incredibly superior to this brother in just about every way. When he is alone, after having spoken with his mother and stepfather/uncle, Hamlet says,

But two months dead—nay, not so much, not two.
So excellent a kin, that was to this
Hyperion to a satyr. So loving to my mother
That he might not beteem the winds of heaven
Visit her face too roughly.—Heaven and earth,
Must I remember? Why, she would hang on him
As if increase of appetite had grown
By what it fed on, and yet, within a month—
Let me not think on 't. Frailty, thy name is woman!—
A little month, or ere those shoes were old
With which she followed my poor father's body,
Like Niobe, all tears. Why she, even she—
O God, a beast that wants discourse of reason
Would have mourned longer!—married with my uncle,
My father's brother, but no more like my father
Than I to Hercules. (1.2.138-153)

Here, he first addresses the timing of his mother's remarriage: so soon after his father's death. Then, he compares her new husband to her old—Hamlet's father was like a god while Claudius seems like a half-goat, half-man creature. Hamlet's father was so loving to Gertrude that he would even want the wind to blow more softly so as not to be too rough on her face, and she would hang on him as though she could not get enough of him. Despite this, it took her less than a month to remarry. He calls all women frail and weak. He says that she had not even broken in the shoes she wore to his father's funeral by the time she got remarried. He believes that even an animal would have mourned the loss of its mate longer than she died. Finally, Hamlet laments that he is as like Hercules as his uncle is to his father: Claudius simply cannot measure up.

Imagine coming home from school to mourn the passing of your dead father. You have no siblings. Most of your good friends are back at school. Who will you mourn with?

Your mother.

What if your mother was to busy being happy over her new marriage?

Hamlet does feel that his father is betrayed, but he also feels that no one has given him ample time to grieve for his father. His mother and his new step-father keep telling him to just "cheer up". Gertrude says: "Good Hamlet, cast thy nighted colour off". But he misses his dad. All of that is tied into his despair.

There is one other consideration. Many critics...