One kind of insult is clearly rp, and whilst you could argue that is rp to punish it, it feels like that act of an arse to me if you do.

The other is someone being an idiot ooc. Either because they are a tlb, or because they are just upset. (One could argue that the two are one and the same.) I do sometimes do a "demonstration punishment" if someone tells me they'll full loot me, but generally I have got over their threats by the time I actually kill them.