To draw a general conclusion on the basis of an inadequate sample of particular cases is indeed a fallacy – the fallacy of hasty generalization. But it is crucial when evaluating some general conclusion to determine what kind of generalization it is, for this will determine in turn whether the sample is adequate and how to evaluate potential counterexamples. Some generalizations are strict generalizations – they claim that every single member of a certain category S has some attribute P. In that sort of case, to find even a single S that is not P suffices to refute the generalization. But many generalizations are what we might call loose generalizations. They do not claim that every single S is P, but rather only that S’s are for the most part P. And here, obviously, to refute the generalization it does not suffice to find single counterexample or, if the class of S’s is very large, even many counterexamples. When people say things like “Women are less aggressive than men,” they don’t mean “Every single woman is less aggressive than any man,” and it does not refute their claim to point to several examples of notably aggressive women and notably non-aggressive men. What they mean is that for the most part, even if not in every case, women are less aggressive than men. Those who treat such claims as if they were strict generalizations and then pat themselves on the back for their logical acumen when they come across a counterexample really only show themselves to be incapable of making a very simple distinction.
Then there are what Philippa Foot and Michael Thompson call “Aristotelian categoricals,” general statements of the form “S’s are P” that convey a norm. For example, when we say “Dogs are four-legged,” we don’t mean that every single dog without exception has four legs, but neither do we merely mean that dogs for the most part have four legs. We mean that in the normal case a dog will have four legs, that every dog qua dog has an inherent tendency to have four legs unless impeded by injury, genetic defect, or the like. Hence, to refute an Aristotelian categorical, it also does not suffice to point to various counterexamples.
In short, you might say: We shouldn’t generalize about generalizations. They’re not all the same.