Some egregious examples that spring to mind are:
* Trying to disprove a point by finding an edge case where it's not true - even if that edge case is entirely irrelevant (a bit like the complaints in the original post)
* Trying to disprove a point by exaggerating it to an extreme and saying that because it doesn't work in the extreme case, it must be false.
* Taking a point out of context and proudly proving it to be wrong... when taken out of its wider context.
* Making an entirely unrelated point which happens to be true, as a way of trying to prove an earlier point.
I guess the second one is a form of hyperbole (but is that the right term)? The third one could be called out as "taken out of context", and fourth is "irrelevant"... but it still feels like life could move on faster if there was a clearer taxonomy for these 'bugs'. (One could even provide the taxonomy as tags/reactions into your communication system of choice - like a more nuanced version of "+5 Insightful" or similar).
Edit: perhaps https://en.wikipedia.org/wiki/List_of_fallacies is what i'm looking for, although it feels... cumbersome.