Firing offense? As in Fort Garry Horse? Leopard II’s? At Shilo? Was that a tank firing offense?
During WW1 trench battles guns were not accurate enough that firing them during an attack made actual sense given the long reload time and chance of malfunction. You could not expect to see an enemy in the trench, much less hit them.
From psychological point of view, however, any sound of shots fired would work as suppressive fire (or deterrant). Hence commanders wanting to perform offensive maneuvers would often order soldiers to a firing offence to limit the enemy fire.
Another interesting tidbit is the term ”deatmatch”, which was not invented by ID software for Quake. It was actually first used as term when a casualty was matched to a missing person.