In nearly every major war, there are a handful of "inciting events" that kick off the war (like Archduke Franz Ferdinand being assassinated leading to a series of treaties kicking in that led to World War I), and in the case of the Gotham War between Batman and Catwoman, this week's Batman/Catwoman: The Gotham War - Battle Lines #1 reveals who is the Franz Ferdinand of this conflict.
Source:https://www.cbr.com/batman-catwoman-gotham-war-inciting-event/