4A Magical Education Is Hardly an Education
Students at Hogwarts are offered a huge variety of classes. We've seen them taking Charms, Transfiguration, Potions ... for some reason Divination and Astrology are two different classes ... there's even some mention of "Arithmancy," which, as a cursory Google search reveals, is some kind of numbers-based divination.
"Yeah, screw summoning my spirit animal. I'd rather do math."
Of every class mentioned in Harry Potter, the only ones of strictly academic value appear to be History of Magic and an optional class called Muggle Studies. At no point do we get the sense that wizardly high school graduates can perform long division, find Vietnam on a map or discuss themes of coming of age in The Catcher in the Rye. What are they learning? They're learning how to turn rats into teacups.
"One day you'll be trapped in a rat-infested shack with company on the way and you'll be grateful for this lesson."
At the end of the day, Hogwarts is a magic school, and the kids who go there are learning magic ... and that's about it.
The Horrific Implications:
Don't get us wrong, magic eliminates the need for a lot of classes -- if Hogwarts students have the ability to instantly teleport, they don't need to learn to drive a car any more than our students need to know how to ride horses. But what about math, or grammar, or freaking sex education? Or any form of biology? This is a world where nobody seems to learn the scientific method -- every problem is either solved by a spell or not solved at all, because problem solving is not a skill that is valued enough to be taught.
"I swear if you make that wand joke again I'll Leviosa your penis off."
We do know they have hospitals -- but only for the magically infirm, which makes us think that Harry Potter's world is one where no one understands the human body or how it functions, because they've never had to learn. No one knows the mathematics behind building houses, because math isn't a thing.
Appropriate Conflict Resolution 101.
You could argue that the wizard world gets along just fine without this knowledge base, since they seem to live comfortably and magic clearly picks up the slack for whatever they don't know. But that's actually shown to not be true, because as we've seen ...
3There Are No Career Options
In the books and movies, every job in the wizard world looks like fun. There are the Aurors (the awesome wizard police who track down dark wizards), the teachers at the school, the owners of the wacky shops in Diagon Alley and the people who work for the Ministry of Magic.
Who basically look like the sort of people you pretend you're out of the house for.
And, um ...
The Horrific Implications:
Yeah, there appear to only be like five careers in the wizard world. When questioned about his aspirations after graduation, Harry's response amounts to a big shrug and contains the word "maybe": "'Well, I thought of, maybe, being an Auror,' Harry mumbled." You can understand his reaction -- the career options available to wizard graduates aren't exactly giving them the world on a silver platter.
"My golly yes, my ambition is to be a heavily disfigured psychological wreck of a man."
Remember, you have to get a magic-related job -- you can't just take a job at some muggle business, since the school system hasn't even taught you enough to work fast food or operate a photocopier in an office. So every career that Harry knew from non-wizard society is pretty much out of the question: engineer, architect, doctor, data processor, plumber, telemarketer, etc. And no, there are no equivalent jobs in the wizard world. Why would they need them?
"So apparently you've contracted Ebola. I have no goddamn idea what that is, so here's some magic flowers."
In Harry Potter and the Half-Blood Prince, muggle-born Hermione explains that her parents are dentists to a room full of people who have no idea what dentists are (because wizards magic their teeth into perfection every day). Likewise, their world needs no carpenters or painters -- in Harry Potter and the Goblet of Fire, some wizards accidentally destroy a wall in a muggle's home and repair it with a flick of the wand -- brick, plaster, paint, all in an instant. Hell, even the reporter in the series has a magical quill that automatically creates prose for her articles. You can't even get a job working in wizard finance -- a race of goblins owns the entire banking system.
It's probably a horrible racist metaphor.
So, yeah, we hope they like teaching or working in civil service, or can get a job working in one of the magic stores that exist in the only two all-wizard neighborhoods in England.