What are hamlets reasons for not killing claudius's?

I think it should be 'Hamlet's' and 'Claudius' for the question to make sense.
Answer:
Hamlet has been informed of his father's murder by a ghost. Now he needs to make sure he's not being misguided by some evil spirit. That's what he tells himself. However he himself says somewhere that he suspected Claudius even before the ghost had revealed the secret to him. He keeps putting off the execution of the murder on one pretext or the other. Once having an easy opportunity at hand he spares the king's life just because he's in prayer. Then he devices this big scheme of confirming the king's guilt by staging a play mimicking the murder of King Hamlet. Even that proves the ghost's accusation. Still he isn't successful in bringing himself to avenge his father's murder. He keeps thinking, confirming and planning but does nothing. In the end he is told that the king has had Laertes poison the sword that he had wounded Hamlet with. This incites him to kill Claudius. It is only in the face of certain death that he finally acts. However, the fact that he knew Claudius had planned his murder, we can still not say that he finally avenged his father's death.
There could be many possible reasons for his inaction:
One- Hamlet is a procrastinator who would evade a final action as long as possible.
Two- His father's death hasn't caused him as much pain as his mother's incestuous relationship with Claudius. Remember he goes into a fit of passion while confronting his mother and kills Polonius in his rage mistaking him for the king.
Three- he does not have it in him to take a calculated revenge just for the sake of his father's ghost. The murders he commits are either to seek revenge for harm intended to his life (Rosencrantz and Guildenstern) or done impetuously (Polonius). Following this trend Hamlet could not have killed Claudius had he not been pushed into a situation where he had no more time to think. He had to act and not for anyone else but for himself.
Conclusion: Since Hamlet himself does not exactly know what his problem is, he keeps deluding himself with all kinds of excuses. This makes it very difficult to pinpoint exactly why Hamlet is the way he is and why he does not do what he does not do.