Cherry-picking refers to the selective presentation of evidence in an argument in order to refute or affirm a point while ignoring other evidence which will not support the point(s) being made. It derives from the obvious reluctance to harvest unripe, or overripe, fruit and to select only those which you will consume.
Often, cherry-picked factoids or references will be over-extrapolated and oversold to give the impression that they are representative when they are not.
Cherry-picking often relies upon anecdotal evidence, because it only uses one or two examples to make a point; statistical cherry-picking essentially use larger-scale anecdotes, by ignoring the broader evidence on an issue.
Quote-mining is a form of cherry-picking, and the genuine points used in the construction of straw man arguments are typically cherry-picked.
Examples of cherry-picking
This happens when someone deliberately selects from a wide variety of material only those items which support the conspiracy theory while ignoring and discarding those which don’t. When this carefully chosen selection of material is then presented as a whole, it easily misleads people into thinking that the conspiracy theory is supported by evidence.
Anti-vaccine activists are notorious cherry-pickers. They will select anything that supports their pre-ordained conclusions while ignoring the majority of evidence that refutes their hypothesis. This is actually the opposite of science, which requires one to review ALL of the evidence before forming a conclusion.