He is using family punishment as a strawman. If you say he is bad because he thinks it's morally praiseworthy to inflict suffering, he will argue that if you like deterrence so much then why don't you inflict suffering on families that should deter them even more lol
Deliberately confounding "reasoning for choice of punishment" and "severity/extremeness of punishment" and "other moral guidelines outside the 'punishment-reason-axis' that inform the option-space of punishment" is obvious rhetorical trolling, who cares what the precise "fallacy-name" is for this sort of behavior.
Now that I think about it from the other end, I don't see how "hurting their family" is excluded from "retributive justice" solely by the definition of "retributive" either. It's been treated as a perfectly valid act of retribution in many cultures across history (and the present day, probably) - see every story about feuding clans killing each others members; they don't do that because they think it's going to dissuade the other clan from enacting their own vengeance in turn.
It's a slippery slope fallacy variant: "if you have laws to deter actions by individuals, then why not have laws which might create greater deterrence" - and then simply assumes all other considerations can be handwaved away.
If the argument: "the psychological harm of knowing there is famine is bad, therefore we should simply kill all people suffering from famine..." sounds ridiculous to you, then so should this person's argument because it's doing the exact same trick.
That's not withstanding the utterly absurd "opposite" he constructs his position as: "I believe in creating suffering as a morally noble goal" is not some sort of counter-argument, it's just him arguing for his own sociopathy in pretty-prose.
There is the argument that making bad people suffer ruins our morality. If we're better than them, then we don't want people to inflict suffering.
The act of torturing someone does something bad to you, regardless of whatever other effect. The kind of person who would torture someone in cold blood is not someone I want next to me.