What's the word for using a general argument that upon inspection does not apply?
Solution 1:
This is simply the association fallacy.
from Wikipedia:
An association fallacy is an informal inductive fallacy of the hasty-generalization or red-herring type and which asserts, by irrelevant association and often by appeal to emotion, that qualities of one thing are inherently qualities of another.
Two types of association fallacies are sometimes referred to as guilt by association and honor by association.