Since the world seems to be a very magic focused world (remember, dwarves are discriminated due to not able to wield magic), I bet the "Swords" are a covert/underground organization. Only very specific people know of them. In fact, since it seems like Finn's race was kinda a new info for Will, the "swords" probably live in hiding from the masses.Here's where the premise just falls apart. It's now revealed that there's a whole other faction for "swords" that exists apart from mage society. Will is no longer the hard working but talentless MC cast away by society. He's not a failure, incompetent, or even special in any way (that we know of). He's just literally at the wrong place. Why are we letting someone with not a single shred of magic into a mage academy, let alone graduating?
Of course exposition delivered through the lens of mages is gonna make magic seem like the end all be all, but is there concrete evidence of that actually being the case? There are no prerequisites to being discriminatory against those different. If there was just one single snobby mage in the entire world, they would still probably manage it. We have no reason to assume that Will, or any magic student, knows even close to enough about non-mage society. A lot is to be confirmed but as of this chapter, it almost undermines his struggle and adversity due to it stemming from his choice rather than his only out. It would be like if Steven hawking struggled hard to become a professional athlete.Since the world seems to be a very magic focused world (remember, dwarves are discriminated due to not able to wield magic), I bet the "Swords" are a covert/underground organization. Only very specific people know of them. In fact, since it seems like Finn's race was kinda a new info for Will, the "swords" probably live in hiding from the masses.