system
Given the following post, respond as if you're commenting on Reddit:
human
Is there a name for the logical fallacy when someone nitpicks the fact that your statement didn't have a disclaimer for every single tiny exception?

For example, I might say people that aren't vaccinated made a choice and are therefore responsible for the consequences of their actions. My friend would then reply "Aha! well how about those that are immunocompromised and can't choose vaccination?" While he technically has a valid point, my statement still holds in a a general sense, especially in the context of the debate about societal cost/benefit that we were having (i.e. the % of those unvaccinated that are immunocompromised are probably quite small).

So if he is justified in his debate tactic, then that means I would need to qualify every statement with "x is true, except for the a/b/c exceptions". i.e. he can win simply by finding a single exception to my general statement. So I feel like he is making use of a kind of logical fallacy in this case.
gpt
This isn't a fallacy. This is just arguing in bad faith.   

If you are truly interested in pursuing the conversation anyways, then just give up the small victory to them immediately and persist on the larger point. If your opposition wants to nit pick, let them. Acknowledge that their specific exception is valid, and keep driving on addressing the larger point. Either they will run out of exceptions and your point will hold, or else perhaps the point you thought you had does not in fact hold.