No one knows where the Amalj'aa animosity comes from but it was mentioned in the Hildebrand quest of all places that during a war with the sister city before it was destroyed (forgot the name) amalj'aa warriors were among the ranks of the ul'dahns. So they were actually allies at one stage.
Most likely reason would be they summoned Ifrit to defend against the Garlean threat and in doing so became tempered and made the world their enemy in the process.