Haven't read the novel fully but from what the manhwa explained briefly...
They're an organization full or at least headed my arrogant people who believe that there should be no mage stronger than them outside of their organization. And thus, they aim to eliminate or recruit/force into joining their group.
The empire's Royal family not only has great physical ability, but a great aptitude for magic(although there are exceptions like Trayle who is talented with the sword but cannot use magic). This is why they are a thorn in the magic towers eyes.
And add to that, that the Grand Mage they were supposed to have as the Master of the Tower, defected to the empire and even married the very strong Emperor and had kids that are just as strong.
And also the Magic Tower are just a group of crazy doctors in a fantastical sense without any sense of remorse and guilt.
Does anyone have any spoilers from the novel? This is boring me but I want to know what happens and why the dark mages won't just leave that family alone.