Why does he kill his daughter?

In my current story, the MC works as an executioner for a rather sadistic kingdom. Public executions are treated like a circus performance almost, with a platform/stage, dramatic music, cheers and boos from the crowd, and even an emcee to play up the scene. Dramatic lighting is controlled via the lighting and extinguishing of various fires and sometimes even powders are thrown in to make the flames change colors. This is a more medieval setting. In the scene, the kingdom has just won a big war and is celebrating via putting on a show (aka massive execution) with the entire local populace in attendance, the king is there, his royal advisers, ect. This is pretty normal and almost routine for the MC. When the MC is given his cue to go on stage for his executions, one of the prisoners from the defeated kingdom ends up being his daughter, who he has not seen in years after she left. The MC can see, by the looks of the king and emcee, that this was completely set up. He knows if he doesn't kill her, the audience will know something is up and he would be waaay worse off since this is ultimately a psychological test set up by the emcee and king (mixture of testing his loyalty and the kingdom just being sadistic). He does end up killing her and getting through his "act" but almost immediately after has a huge meltdown.

Basically, I don't know what psychological reasoning/persuasion he used on himself to do this. It's a rather short-ish story and doesn't need to be overly important in the long run. Any and all ideas appreciated!

Because he was raised in this sadistic culture. I'd be surprised if he didn't kill her, since presumably he has the same values as the king and emcee and everyone watching this execution.

If he has an emotional attachment to her, he may be wanting to spare her from further pain. After all, she is a prisoner. Chances are, she would die whether or not he killed her. At least if he kills her, he can control how quick it is.