In retrospect, feel free to skip to the last section, lol.
Interesting Philosophy
An interesting philosophy class should probably include...philosophy, but taught in an engaging way (whatever that means) while also including interaction/participation from the class. You've got many people in the room, but only having the teacher speak would be wasteful.
In story terms, that'd be: character interaction and development where the exposition is mostly philosophy ideas, and then tying those ideas into the characters.
With a storygame, choices can offer the reader options that they can use to better learn the material, but writing this way would be difficult (the only way they'll be learning by is through reading as well). Everything is prewritten and cannot be in any way shaped for the individual (but you could just have a broad number of variations, but how you'd figure this out is a bit beyond me). Not all schools are equal anyway...
A better option might be having the material exhaustively explained in so far as it is relevant for the story, without any 'learning' choices (or perhaps minimal learning choices instead). Then again, plenty of philosophy things have relevant texts, and I don't know how readers would feel about having to read a book to read a storygame. On the bright side, surely some of the books are public domain, so you could just include them in your work, lol.
Debate sessions are neat, but I do think they can fall flat. The need to think fast and know what you're talking about are both removed when debating in a storygame, where there is no time pressure and all the options are visible. Tight writing can help keep this engaging despite this. 'Wrong' options can also add back some need to know what you're talking about. Tying debates to the bigger narrative could also help.
Scope & School
How in depth you go with 'teaching' is worth thinking about. You said you wanted real subjects and real exams, but that is a LOT of work. Schools are ran by multiple people, but you'll be writing this yourself, and I'm not sure you've got the qualifications (which isn't a major issue in the sense you need to be a teacher to write about a school, but rather that you might not know things that'd be important regarding creating exams and subject curriculum, but you do have access to the internet!).
If you're motivated, I wouldn't worry about this. However, not having your scope be too big is instrumental in helping finish things. Stopping scope creep is worthwhile regardless, and so thinking about your scope thoroughly could be beneficial. A story that spirals out of control can suffer greatly in its quality, which is bad enough without even considering that they might just never get finished because of it.
What timespan are you covering? A year of classes? Half a year? One class till exam? School takes a long time to get through, aha.
Keeping it focussed on Philosophy seems like a good option to me. The characters still take Math, English, etc, but you skip over these elements, or just have short sections (?). Lots of options in how you handle this.
Accessibility
Philosophy itself can also be a bit inaccessible, so picking a good starting point is important. What actually is philosophy? How are arguments constructed? etc. You might want to jump straight to Derrida or Saussuer, but if you do, consider if there is any groundwork that some readers may not be familiar with that'd be beneficial to include.
This ties in with scope.
Looking at the ideas but also their shortcomings is important for philosophy, but with a story you can do this in some more interesting ways. Having characters show where certain theories fail, due to their circumstances or actions, and the like. (Also the opposite, where they affirm theories). Readers choices can do this as well.
The examples you provide can be more emotionally charged than pure hypotheticals that'd you'd get outside of a story (readers will get more invested in your characters than some random 'person A' they make up for a counter example).
Doesn't Even Matter
Anyway, you're already half-way through, so no idea why I'm talking about this as if you haven't started (or written only a little).
Being half-way through, I'd say just keep going. Revisions can be made at the end to fix up any weaker areas (even if revision aren't everyone's favourite thing...but they are powerful!).
My main advice would be to think of how you can have your endings tie in with the philosophy themes, as that can help them feel more impactful while also tying everything together (assuming this works for your story, of course).
P.S. I almost included a section regarding storygame structure (variables or no, and how that could impact delivery of this type of storygame). That would've been extra useless at this stage.
Edit P.P.S. Oh, here's Gower's article on dialogue punctuation. Something to look over before your next proofreading. Let us know if it makes sense!
Edit 2 P.P.P.S. At a quick skim/glance, it seems you're not using variables, but the way you've structured stuff seems to really scream for there to be variables. Oh, you made a thread asking a question about this, never mind.