Argument By Generalization:
drawing a broad conclusion from a small number of perhaps unrepresentative cases. (The cases may be unrepresentative because of Selective Observation.) For example, "They say 1 out of every 5 people is Chinese. How is this possible ? I know hundreds of people, and none of them is Chinese." So, by generalization, there aren't any Chinese anywhere. This is connected to the Fallacy Of The General Rule.
Similarly, "Because we allow terminally ill patients to use heroin, we should allow everyone to use heroin."
It is also possible to under-generalize. For example,"A man who had killed both of his grandmothers declared himself rehabilitated, on the grounds that he could not conceivably repeat his offense in the absence of any further grandmothers."
-- "Ports Of Call" by Jack Vance