1. Guilt and Fear: Claudius is deeply aware of his own guilt in killing his brother and marrying Gertrude. Hamlet's constant mourning and melancholic behavior serve as a constant reminder of his crime and the potential for exposure. The more Hamlet dwells on his father's death, the more likely Claudius is to be unmasked.
2. Threat to Power and Stability: Claudius's reign is built on a foundation of deceit and murder. He needs to maintain the illusion of legitimacy and stability to secure his position. Hamlet's public grief and erratic behavior disrupt this facade, raising suspicions and potentially destabilizing the court.
3. Personal Discomfort: Hamlet's grief is intensely personal and deeply affecting, making Claudius uncomfortable. He sees it as an unwelcome intrusion into his own carefully constructed world and a constant reminder of his own moral failings. He wants Hamlet to move on, to be "more man and less a woman" (Act 3, Scene 2), so he can be free to enjoy his newfound power and pleasure.
4. Fear of Madness: Hamlet's actions and pronouncements often border on madness. Claudius is unsure if Hamlet truly is mad or is feigning it as a means to expose him. This uncertainty adds to his anxiety and reinforces his need to silence Hamlet.
5. Loss of Control: Claudius is a master manipulator, used to controlling the court and manipulating people to his advantage. Hamlet's unpredictable nature and resistance to control frustrate him. He wants to understand Hamlet's motives and to regain the upper hand in their psychological battle.
In essence, Claudius's irritation is a complex mix of fear, guilt, discomfort, and a desire for control. He fears Hamlet's potential to expose his crime, disrupt his power, and threaten the stability of his reign. Hamlet's grief is a constant reminder of Claudius's own moral failings and serves as a powerful symbol of the consequences of his actions.