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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.
The fallacy occurs by processing an analogy in the following way:
A is like X in some way
B is like X in a different way
Therefore, A is like B.
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.