Did you miss like the entire storyline? They never went to war over Garnet! Brahne when to war to gather the Crystals since she knew of their destructive power, which is very believable.
Did you miss the whole of the first disc? Regent Cid sent Zidane and co to kidnap Garnet because they suspected Brahne of something (mainly due to her meetings with Kuja). Regent Cid did this because he and the late king of Alexandria were best buds. and Kidnapping a princess will be seen as an act of war.

it is after that that Brahne decides to engage the plan of the Crystals

How many times have countries went to war over resources to make themselves more powerful?
Don't mention ze voar! lol