Is there a logical fallacy for when someone uses an extreme example

Hi John,

See the nutpicking fallacy .

There are a few that could possibly match. Obviously, it's not an exact science as it often depends on how the claim is composed. Personally, I love Doc's proposed "nut picking" fallacy. I must admit I haven't heard that one before.

From the examples provided (arguably), I  thought of the Hasty Generalization,  Composition Fallacy e.g. that which is true of the part is true of the whole, and perhaps more loosely Ad hominem (guilt by association).

While in line at the unemployment office, I saw nothing but work-shy layabouts applying for benefits,

Therefore anyone who claims benefits is really nothing but a work-shy layabout.

Isis K, Al Qaeda, Boka Haram are Islamic terrorists and Muslims.

Therefore all Muslims are potential Islamic terrorists.

Nutpicking, as Dr Bo suggested, is a good answer.

The Appeal to Extremes you mention refers to a failed Reductio Ad Absurdum (a valid logical technique), where instead of showing that an argument leads to absurd conclusions, the argument is distorted in order to make it look as if it produces absurd conclusions (this is similar to the strawman fallacy).