I'm looking for the name for a particular logical fallacy that I think of variously as the "philosopher's fallacy" or the "annoying middle school kid fallacy", based on the particular informal contexts where one is most likely to encounter it. A more specific name might be the "fallacy of underwhelming exception".
It's sort of like the reverse of the fallacy of accident.
Where the argumentative fallacy of accident takes a broadly accurate generalization and misapplies it in a specific context where it becomes invalid, the fallacy I have in mind seeks to cast doubt on a broadly accurate generalization by nitpicking a particular instance where it fails.
I also see it as being the flip side to the "overwhelming exception" fallacy: instead of a 'generalization' that's overwhelmed by so many caveats it ends up lacking any generality, it's a purported refutation of a generalization, but one that's so underwhelming that it actually underlines the reliability of the original generalization (hence "underwhelming exception"). Here are some instances:
Teacher: "You shouldn't talk during class."
Annoying middle school kid: "But what if there's a murderer behind one of our classmates, and we need to warn them? It'd be okay to talk during class then, right?”
Regular person: "It's wrong to murder toddlers."
Annoying, slightly older middle school kid: "But what if, like, you could see the future, and you saw in the future that the toddler was going to grow up to be, like, Adolf Hitler times a million? It seems like sometimes, like in a situation like that, you might have to murder toddlers. Why would you say it’s not okay? Why do you hate Jews so much?"
These can come up in social justice-type discussions, as well:
Sociologist: "Mainstream media outlets often manipulate the public via appeals to sexuality."
SJW: "Um, you're erasing asexuals, and hemicorporectomy survivors. Are you saying we don’t need to take them into account in sociology? Why would you write off entire groups of people as irrelevant and unimportant? Sounds acephobic and ableist, but okay....”
But almost any discipline in philosophy worth its salt is structured around one or two paradigmatic instances of this fallacy. An obvious one is the trolley problem in moral philosophy:
Regular person: "It's wrong to deliberately kill innocent people."
Philosopher: "But what if there's 100 innocent people tied to a trolley track, and a single innocent person on a side track, and you can save the 100 people by switching tracks, at the cost of killing the one person? It'd be wrong not to kill the one person, right?"
Or take the classic JTB account of knowledge in epistemology:
Regular person: "Knowledge is justified true belief."
Gettier: "But what if I intend to watch the 1998 NBA Finals live, but I accidentally watch the 1997 NBA Finals where the Bulls beat the Jazz 4-2 on VHS, and meanwhile the Bulls really do beat the Jazz 4-2 in the 1998 Finals?
I believe that the Bulls are the '98 NBA Champions, and it's true, and I've justified my belief by watching the Bulls win, but my justification was accidentally bad, so do I really know that the Bulls won in '98?"
What is the name for this kind of informal fallacy, where a picayune, innately hypothetical, farfetched, or just plain impossible counterexample is implied to severely undermine, or outright disprove, a widely valid generalization?