Proposition: Pointing out that rare exceptions exist is usually a negative derailing tactic. However if you think your conversational partner is annoyingly pointing out a rare exception, double-check in case they think they are pointing out a common exception.
Human space is deep and wide, and there is a lot more variation in humanity than we really give credit to. This means that for almost any generalization you can make about people, there exists exceptions to the rule.
One rhetorical trick people sometimes use is to point out rare exceptions when the discussion is focusing on generalizations. For example, let's say Alice argues that five year olds shouldn't be allowed to vote because they aren't mature enough or knowledgeable enough. Bob replies "Some five year olds are more mature and knowledgeable than some thirty year olds."
Well... it's strictly true, in that there are some five year old prodigies that you could compare against some non-functional adults in a vegetative state. But it isn't really helpful to the conversation, and it tends to be derailing. This is a case where you are searching all of human-space to find your 0.001% exception and then going "AHA!"
However, there are also times when there are many people who fall outside the norm, and pointing out the exceptions is useful. If Clair says they don't use women to stock shelves because women aren't tall enough to reach the top shelf, and Derek points out "Some women are taller than the average man," this seems very different than the previous example. It would be rare to find a five year old that is more mature than a thirty-five year old, but not at all particularly rare to find a woman who is taller than a man (even though on average men are taller).
I think sometimes misunderstandings occur when one person thinks they're pointing out a common exception, and their conversational partner thinks they are pointing out a rare exception. Maybe Bob really thinks that something like 10% of five-year-olds are more knowledgeable than about 10% of adults. If Alice assumes Bob is just pointing out the 0.001% exceptions that always exist in all human things ever, she is going to be more likely to assume Bob is arguing in bad faith, and miss out on finding their true disagreement.
(I am bad at naming things, if anyone has an idea for what to call it when you point out a 0.001% exception.)