The protagonist in William Shakespeare's' Hamlet is Hamlet. As the main character he faces many problems. His biggest problem is his internal conflict of whether to kill his Uncle Claudius or not. There are many reasons as to why Hamlet want to and then hesitated in killing his Uncle. He had his doubts. Was the ghost good of evil? Did is speak the truth? Is killing really the right thing to do? Hamlet's delay in killing his uncle is understandable. .
Hamlet has his reasons for wanting to kill Claudius. The foremost one being that Hamlet suspects Claudius of killing his father. One's father's murderer is certainly someone one would want dead. Another reason Hamlet would wish Claudius dead is that Claudius marries and lusts with Hamlet's mother. This sickens Hamlet, giving him another reason to want to kill Claudius. From things Hamlet says we know that he finds his uncle totally despicable and ignominious. He says "My father's brother, but no more like my father than I to Hercules." (Act I, scene 2) Claudius thinks that Hamlet wants him dead because Hamlet wishes to take the throne. So there are plenty of reasons for Hamlet to want to kill Claudius. However there are also many reasons for Hamlet's delay in killing Claudius. .
One reason for delay is he's just seen a ghost. That alone is terrifying enough. Seeing a ghost on earth is a major upset in the natural order of those times. Hamlet doesn't know if the ghost is good or evil, from heaven or hell, or honest or deceitful. Therefore how can he swiftly act upon the ghost's words without having any doubts? Encountering a talking ghost is reason to question things. .
Another reason for not acting on the ghost's words would be that he's being told to kill royalty. Royal murders receive more publicity, repercussions and consequences. All royally affect the people around them. They cannot help it. It's like being a whirlpool. Everything in a whirlpool's path is influenced by it.