I'm looking for a succinct way to describe what I believe is a semi-common situation, both in online discussions and sometimes in real life (e.g. with siblings during long car trips): when a discussion between two or more people turns sour, such that rather than discussing or debating the subject at hand, the people involved get sufficiently irritated with each other that they instead get drawn into a back-and-forth series of pointless/petty/passive-aggressive criticisms of each others' style, grammar, minor logical ambiguities, etc.
I might call this "hen-pecking" (in reference to possibly-apocryphal reports that chickens packed into too-close proximity with each other will eventually start pecking each other to death, and must therefore either be given more space, or fitted with red contact lenses to calm them down), but I think there might be a better, more well-known phrase that describes the phenomenon. Can anyone supply such a phrase?