Ah yes, murdering their leader after coming to him with the pretenses of diplomacy -- that would surely sway the Garlean people to your side. After all, the average Garlean trusts you implicitly! Just think back... oh, two quests ago when three starving men shanked Alphinaud behind the house so a defenseless girl could take her crippling ill little sister and flee to the monster-infested ice fields because they'd MUCH rather take their chances there than with you, and that's after you've all already helped them.
To put it another way: three men went on an agreed suicide mission to act as a short-term distraction so two people could almost certainly die to wolves and monsters in the freezing cold -- because they are 100% absolutely positively sure you'll do far worse to them.
The Garlean history is one of oppression, misery, and overall getting their butts kicked to the frozen wastes by the other, magic-using races. This breeds resentment. Resentment turns into nationalism. Then, when given the means to not just fight back against their oppressors, but to conquer them in turn... all in the name of peace, mind you. The savages can not be trusted, and the only way to ensure peace with these monsters is to subjugate them, or exterminate them.
Is it right? No, of course not. But this is what generations of Garlean people believe, and it's all they know. To them, these magic-wielding foreigners are just trying to subjugate them, to destroy their national identity and who they are at their core. This is, of course, because that's how they operate. If the Garleans encountered a severely weakened enemy city, they might buy their way in with promises of aid, only to take everything from them when the opportunity was right. Look at Ala Mhigo. The nation just finished a devastating civil war, and in swoops Gaius and the fleet to seize control right after. (Convenient timing, isn't that?)
Oh, and everyone's favorite totally-not-a-bad-guy Emet-Selch is the one who put all of this into motion. Don't forget that.
Edit - Oh, and how could I forget the girl there who recognizes you by face. She saw you AOEing down dozens of her friends like they were nothing in Castrum and Praetorium. 8 Eorzeans butchered their way through over a hundred people and warmachines and barely even stopped moving. Then, for good measure, you blew the place to hell before most people had a chance to evacuate. (The only people who could possibly have seen it was the Ascian and Ultima Weapon that blew the place up would have been caught the blast.)