This is the dumbest thing i've seen in a manga/manhwa, and i've seen alot.
You want food for your people, sure, threatening war if you don't get it would have immediately ended negotiations in a situation where the western empire had the upper hand in negotiations like this, and likely a declaration of war by the west.
It also has no logical beneficial outcome for the east, if you somehow win a war with your weakened army, it's likely the west would burn their own fields just to prevent you from getting the food out of spite, the romans were known for salting fields and poisoning wells in wars exactly for this reason, this was a no win argument for the eastern empire, so i don't even know why they even suggested it.
Not only that, but even the suggestion of conflict means that they have a desire to conquer your lands, this in turn means no matter if you help them, they can NEVER be trusted and will likely wait for a moment of weakness to attack you, it boggles the mind.