Creating a straw-man by cherry-picking extreme outliers of large data sets, e.g. using Caligula as ‘proof’ that the Roman Empire was uncivilised, and going on from that to say that all ideas and artefacts from the Roman Empire should be discarded.
(I can think of plenty of examples from the modern world, but if I actually name one then someone will misunderstand and/or believe the thing which I would call a straw-man and mistake the cherry-picking for a valid data-point — I’ve seen this happen quite a few times online).
There’s got to be a better name for this — it’s coincidentally the name of at least one real person — but I can’t think of one.
Edit: “Nut picking”, a neologism coined by Kevin Drum, Wikipedia attributes it to The Washington Monthly, (August 11, 2006).