Name that logical fallacy segment:
I think the listener's friend is actually begging the question. Since we didn't get the details, I can't be certain, which means I'll have to speculate a little. But it sounded to me like the sort of move the friend was trying to make is begging the question for whatever it was s/he was ultimately trying to argue for. We know that s/he wasn't simply arguing that being a rule or law is sufficient for being fair or just, because s/he wouldn't accept that the death penalty was "on the same level", so to speak, as whatever rule or law that s/he was referring to. So there was some rule or law of interest, and it was likely intended to be playing a role in some set of premises for some conclusion. The combination of, (i) claiming that being a rule or law is sufficient for fairness or justice, and (ii) claiming there is some inherent difference between the death penalty and what s/he is referring to that makes them incomparable, is a move that sounds to me like it would only make sense under some assumption or set of assumptions that is already (probably theoretically) connected in some way to whatever her/his conclusion is. Begging the question is kind of like trying to get a free ride to the conclusion without anyone noticing you didn't actually pay the fare.