Why can't Hamlet kill Claudius immediately after he founds out he killed his father?

Hamlet doesn't really want to kill anybody, which is why he always makes excuses for it. yes, he hates Claudius, but Hamlet is catholic and has been raised to believe murder is the ultimate sin. It's not something he would do lightly, especially not when he's unsure whether to believe the ghost or not. If you mean the scene after the play within the play, he lets Claudius go because he's praying, and if he dies while praying he would go to heaven.