Very related: Is President Snow sadistic or simply ruthless?
At the end of the Hunger Games movies when President Snow is facing execution with Katniss's arrow, Snow could be seen grinning malevolently and quietly encouraging Katniss to "let it fly." Why did he do that? Given that he'd die in the process, what could he possibly hope to gain by her doing that?
Did he believe that she'd somehow cause herself suffering or discredit herself in the process? If so, why did he care? Based on the linked question, Snow appears to have been ruthless, not sadistic, so what did he care if she suffered after he was dead?