The White Raven, Legatus Nael van Darnus of the House of Darnus managed to convince his Radiance, the Emperor of Garlemald, to utilize Dalamud, a weapon of mass-destruction akin to a nuclear missile, to eliminate Eorzea completely.
This sounds essentially insane, and even others in Garlemald clearly believe it to be a bad idea. Cid, who was probably a superstar in the empire due to being responsible for a great deal of their technology, left because of the incident at Bozja citadel. And Gaius van Baelsar makes it very clear that wiping out an entire land is counterproductive and useless.
Let us consider the history of Garlemald.
For years it was nothing. Insignificant and not a world power. However within a century (50 or so years i believe), it managed to became one of, if not the largest, powers on Hydaelyn. It's rise was a result of a massive and rapid technological advancement, and an ambitious military restructuring by a legatus turned emperor.
The social structure seems to be one similar to ancient Rome, with family houses playing a prominent role as societal regulators, and a strong honour code. Those who excel in a house (so far we only know of males) seem to become Legati, which are essentially generals of legions. These legions are loyal to their Legatus, and not necessarily to the emperor, as we can see with the 7th legion searching for Nael van Darnus believing him not to be dead after we kill him.
Further, rapid expansion comes at serious costs. Regardless of their technological advantage, the empire faces dwindling military forces resulting in a policy of conscription, and constant rebellion. Further, it is clear that while the empire -projects- power, they face multiple threats from multiple directions.
Eorzea seems to be a particular problem. It is revealed by van Baelsar that the eikons (primals) are the reason why he hasn't been able to conquer Eorzea. This is most likely why he lost favour with the emperor, who took the White Raven's side in utilizing meteor.
But if Eorzea is no threat, why bother destroying it -completely-. It is clearly costing a lot of resources and soldiers lives to pull it off, and the Emperor and van Darnus both clearly know it will eradicate the land.
To understand this, we have to understand the culture of which would arise in Garlemalds situation. It is most likely well known to Garlemald that Eorzea's history has been forged in warfare. The holy see (the greatest military power in Eorzea) is in constant warfare with Dravania and the dragons. In the past all the nations have faught each other, the beastmen, etc. Many of the battles between Ishgard and Gridania are mentioned throughout the game for example. And the beast tribes clearly state that in the past when they attempted to have a peaceful existence the 5 races screwed them over.
So in Garlemald the average person is probably aware of Eorzea's bloody history. Further, the primals in Eorzea are clearly a threat to the Garlean empire as they block their expansion, and they are essentially insane. We get to meet ifrit and garuda, who are both -nuts-. They are power hungry beings with no problems killing those that get in the way. Further, the Allag civilization clearly has technology buried around Eorzea as van Darnus utilizes it to summon meteor.
Garlemald also seems to have dropped religion. The Legati are pretty clear that the gods people worship ignore them, and that they are strongly against eikons, which is a derogatory term for the primals insinuating that they are false gods and just monsters. Essentially, the gods are dead to them.
So you essentially have a land full of pirates, merchants, and extremist forest dwellers near your homeland borders. As well as an incredibly extremist religious nation (Ishgard) who has a massive military force and is in proximity to ancient technology. Further, you know 100% that they can form a military alliance, as they have in the past. There are also beast tribes who can summon beings that believe themselves to be gods, who are a serious threat to your nation. And years and years of military endeavors by someone essentially obsessed with the conquest of Eorzea have proved futile. You then have paragons and such going around promoting the summoning of these primals.
It's no surprise that Garlemald developed racist ideologies to those associated with primals/eikons who believe themselves, and would seek to make themselves gods. Further, it's no surprise that Eorzea is viewed as a significant threat.
A technological culture with rapid expansion facing multiple cultures who strongly believe in gods is bound to result in an engrained obsessive racism, and the cultural acceptance of WMDs. And as such, in a way, Garlemald is not a horrible narcissistic nation bent on world domination, but rather a product of rapid advancement and unavoidable societal tensions as a result.