You don't want to be part of the X-Men
For the young mutant, the Xavier School for Gifted Youngsters seems like the dream. That is the place you want to be educated. You can be amongst other mutants, you are taught by the X-Men, none of this is bad. But in reality, the Xavier School for Gifted Youngsters is quite possibly the worst choice you could make in your young mutant life.
You get to your teenage years, and you wake up one morning. You get out of bed, shower, eat breakfast, and put on your clothes for school. Between the time you do that and the school bus arrives, your pants get wet. What's going on? Well, over night, your latent mutant powers have manifested and it turns out that you can brew coffee in your back pocket. It's embarrassing and you find that being at school is becoming increasingly difficult as you can't yet control your power (and what a power it is) sufficiently so you have to bring extra pairs of pants to school with you all the time and other kids find out and they start to beat you up. First, because you are a mutant; second, because it's a weird power to have and it makes you keep wetting you yourself; and third, because kids are cruel like that.
So you beg and plead with your parents to apply to the Xavier Institute for Higher Learning. They relent and one day a few weeks down the track, an envelope arrives. You've been accepted! They do warn you that you will be part of a team that has equally bonkers, and niche, powers as your own but they hope that the team will be able to work together as some insane Rube Goldberg machine. You'll often have to sit on the bench but when that villain comes along that calls for a combination of back pocket coffee, the ability to levitate a foot off the ground, and being able to turn A5 envelopes (and only A5 envelopes) into miniature rabbits that can hop around and everything, on that day, you and your team will spring into action and you will be a bona fide mutant hero. Huzzah. Christmases. They've all come at once. Right?
No.
In New York State, accreditation for private schools is not necessary. Registration is optional. However, only private schools that are registered can issue diplomas. If the school isn't registered then any diploma that Professor X is handing out may as well be a piece of paper that you have scrawled “I done learning things good” on in crayon.
Let's assume it is registered. The New York State Regulations on issues such as teacher certification and curriculum are fairly black and white, so it's a stretch to say that the school would automatically have passed registration. Which means that if the school is easily passing registration and passing any visits by the state's Bureau of School Registration then Professor X and his mind controlling ways are behind things.
Sure, the X-men will teach you how to be able to control your power. You'll be a grade A barista direct from your back pocket in no time at all with their devoted tutelage. But you won't know much beyond what they taught you in elementary school. All the teachers at the school only seem to have the qualifications of:
1. Are a mutant.
2. Went to the school themselves.
3. Haven't died in one of the many numerous attacks on the X-men.
None of them seem to have formal teaching qualifications in any subject whatsoever with maybe the exception of Hank McCoy (cause he's a doctor and that means he's got himself a PhD) and Professor X (but whether he is an actual doctor, an actual professor, or is just some guy with crazy strong powers who tells people he has an advanced degree is a point of contention) and Jean Grey (who at least as far as the movies is concerned is a doctor).
This is a rather large issue. To pass registration, one of the requirements is that:
“Instruction may only be given by a competent teacher.”
It is feasible that Cyclops went out and got his teaching certificate. That he spent years at night school studying part time, working his schedule around other commitments like saving the world when duty calls and being interrupted by mutant crises while trying to poorly teach young mutants as an uncertified teacher. It's completely possible, there may even be an X-book out there all about that. However, it's unlikely for just one of the staff, let alone all of those that don't already have advanced degrees.
Just what exactly are these unqualified 'teachers' going to be teaching? Given that the teachers' specialities often seem to come from their powers a rough curriculum probably is:
Advanced Weather with Storm
Introduction to Laser Eye Glass Manufacturing with Cyclops
The History of Sparkly Things Like Fireworks with Jubilee
Onomatopoeic Retraction of Claws with Wolverine
Advanced Healing with Wolverine
Science with Beast
Thing is, again the New York State Regulations lay out what must be taught as the curriculum:
“Beyond the first eight years, instruction must include the English language and its use, civics, hygiene, physical training, American history including the Declaration of Independence and the Constitution of the United States, and may include a course in communism and its methods and its destructive effects.”
So graduation day comes and you get your diploma. Huzzah. You are a high school graduate from a questionable, exclusive, exclusionary private school. There are three options you probably have now:
1. You could stay on at the school and become another 'teacher' perpetuating the cycle of dumb people teaching young people dumb stuff. But without being a main character in a current X-book your chances are slim.
2. The military always loves a good trained soldier. Which is essentially what you have been taught to be during your time at the school. You are a human weapon. Or you would be, but brewing coffee won't really make you much more valuable out on the battlefield than your average grunt. Secret Black Ops programs are hardly going to want you either.
3. A dead end job. Maybe two of them to pay the bills.
That's you my young mutant friend. Sure you finished 'high school' but the school wasn't much to write home about and that's if somehow you've been able to learn to write at all.