Hamlet decides against killing Claudius because he represents his innermost desire to have a sexual relationship with his mother Gertrude. Hamlet would also be murdering a part of himself if he killed Claudius.
In Act Three, Hamlet once more questions whether to kill Claudius because he believes that if the man dies while praying, his uncle would enter Heaven.
Because he didn't want Claudius to enter heaven, Hamlet refrained from killing him. He wasn't convinced his uncle was guilty at first, so he didn't purposely try to stab an innocent man. Hamlet was completely certain after seeing Claudius' reaction to The Murder of Gonzago. However, an opportunity to murder Claudius appeared when he was in prayer.
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