Publically known reason for war: Want to have revenge on Liberty and Bretonia for getting betrayed back in Sol.
Why? Because those two operated to use the Gallia (sleeper ship) as a decoy for Coalition forces. (Even though the other three sleeper ships profited from that too, their nations didn't take part in this operation.)
Actual reason for war: Want to get more and more resources.
Why? Because Gallia managed to run out of their own and spent their last reserves on a massive war machine to conquer space for resources. (Yup, while everybody might think Gallia is a Mary Sue, all winner House without weaknesses, well that's their weakness. A Blitzkrieg favors them the most, but get exhausted fast from a war getting longer.)
Naw it's all a Coalition conspiracy to weaken ALL the houses for a sector-wide revolution. But in all seriousness, Gallia is resource-starved, they are DESPERATE for raw materials considering they pretty much went all-in on their war-machine and see the Sirius sector, particularly the Taus and Bretonia as a life-line, all they had to do in their minds was be bold enough to take it. The problem with the current state is that it's so stagnant at the moment, neither side has made any real gains/losses since the fall of Leeds, but that could be due to a fear of the general playerbase on any 'changes' that could disrupt their status quo or the fear by individual factions losing something they feel is vital to them and unwilling to put forth the RP effort to really fight for it in an event. Every faction in Sirius is guilty of this which is why things don't tend to change hands often and when something DOES change it brings about endless complaints from the faction & their allies who stood to lose said property.