Generalizations can go wrong in all sorts of ways. Let's try to get them right.
The right way
If you say something unambiguous:
- members of the group referred to are easily distinguishable from non-members of the group
- your claim about the group is unambiguous, precise, and accurate
that would seem to be correct.
How this can be screwed up
Those criteria for correctness can be screwed up:
- members of the group referred to are not so easily distinguishable from non-menbers of the group
- your claim about the group is a,ambiguous, imprecise and/or not accurate
Distinguishing members from non-members
Often times, groups are referred to using vague labels (possibly due to laziness, indistinct thinking, and/or the poverty of our language). This can leave people wondering. It also leaves open the possibility for bias in hypothesis testing, such as the sharpshooter fallacy, where that ambiguity is "resolved" into precision only after the test has occurred.
As time goes on, I could probably study more ways this criteria can be screwed up.
We need fairly precise claims so that we can test them, basically.
If the claim is too vague, a test might either not be possible, or different interpretations of the claim will exist (some might be true/accurate when tested, some might be false/inaccurate).