Extended analogy

Extended analogy is a logical fallacy where the use of an analogy (a rhetorical device used to compare the same phenomenon in different contexts for emphasis or clarification) in a discussion of a general rule is taken to be a statement that the scenario in the analogy and the scenario in the original argument are alike in additional ways. It is a fallacy of distraction.

Form
The fallacy occurs by processing an analogy in the following way:

The fallacy will focus on unacceptable aspects of the final line in order to ignore the purpose of the comparison. For example:
 * Person N: "Software pirates should campaign to change the law and not break it. I don't think it's ever valid to oppose the law by breaking it."
 * Person M: "Such a position is odious: it implies you would not have supported the women's suffrage movement."
 * Person N: "Are you suggesting piracy is as important as giving women the vote? How dare you!"

M's analogy is a valid reductio ad absurdum response to the original argument (that it is never acceptable to break the law while opposing it), but N's reply instead assumes M's analogy is a claim both acts are equally significant.

This fallacy occurs particularly often with comparisons to dictators, such as Hitler. A tobacco company may, for example, point out that Hitler was adamant that tobacco was unhealthy, implying that thinking tobacco to be unhealthy is the same as hating Jews. However, this tendency allows us to further demonstrate the fallacy by inverting the situation for a moment: imagine if someone in the Soviet Union compared Stalin to Hitler because they were both horrible mass-murdering leaders, and Stalin took it as a comparison of their mustaches. Stupid, right?

Honestly, this is probably one of the dumbest fallacies you can commit; Even kids watching Sesame Street understand that just because the puppet says that the yellow square and yellow circle are the same color, it doesn't make them the same shape too.

Counterexamples
While this may fall victim to Poe's Law, an extended analogy may be deliberately absurdist for the purpose of creating a joke. (For example, Josef Stalin would be quite justifiably offended at having his mustache compared to Hitler's.)

Additionally, any scatological analogy ("full of shit", etc.) can easily be tied back to a corresponding Freudian diagnosis ("anal-retentive", etc.). Whether these cases are evidence of overextended analogies on the part of Dr. Freud is left to the reader's judgment.