You're a transfer student there to learn how to hunt mages and how to identify their magics. Probably put there by a government body of sorts that helps police casters in the world.

Y'all got any other ideas? :3

You're trying to learn about magic, even though you can't use it yourself. Maybe the job you're hoping to get requires some knowledge of how magic works, or you even want to teach at Strixhaven after you graduate.

The same reason a business major goes to MIT. Because magic is useful, even vital, in their daily lives (this is true for almost every PC who is not a solo adventurer and even some who are). I have a character who is a barbarian attending classes at Lorehold and she was actually inspired by an example in the book.

Maybe your magic is different, or your capabilities are similar to magic but aren’t quite magic. Psionic races and classes could be looking for answers regarding their own powers by looking into forces that seem to parallel their own.

I could see soul knives and psi warriors looking for help and guidance with their powers, similar to perhaps sorcerers in a way.

If you were to compare magic to language, then you could say that a student that studies magic without using magic is like a student studies linguistics and not how to speak a specific language. 

Or maybe they're interested in the history of magic rather than its application. 

Or you could even say that they do practice some magic, but it's just not what you'd call "adventuring magic" like in the handbooks, rather it's more highly niche and theoretical and not the kind of thing that's of use in an adventuring sense-- like spells that can tell the positions of subatomic thaumaturical particles moving through the Weave-- that kind of thing that's pure roleplay and doesn't impact your class. 

Those are just a few ideas. In the novel Johnathan Strange and Mr Norrell there is a whole subset of people who study magic but don't actually practice any (though the book takes a dim view of most of them) if you're interested to see what that looks like. Just a great book in general. 

If you're looking for a more mechanical answer I'd say there's a solid two step process for making a character of any class work in Strixhaven: Step 1, make a character of any class. Step 2, as soon as you can (lv 1 if v.human or if your dm gives out lv 1 feats or at lv4 otherwise) take the Ritual Caster feat. Done.

I was under the impression that this was what the Strixhaven backgrounds were designed for... basically they give you some rudimentary magic to justify why your character is attending Strixhaven without requiring you to play a spellcasting class.