"Perfect analogy" fallacy

I have seen this used many times when it makes sense. Typically, it is when people are, as you said, offering weak analogies. I have a difficult time seeing this as a fallacy. It seems more of a lack of understanding of what an analogy is and how it works. We have seen this with the "you can't compare covid to the flu" people. Of course you can! What one can't do, is claim two things are similar when they are not. So when people say "You can't compare X with Y" I really think they are just not being precise with language. They really mean that the comparison made was weak or perhaps there are so many differences (or differences of such significance) that the comparison is pointless.

I agree that it should be mentioned because people use that kind of objection to play it dumb. It's like strawman in a sense that they purposefully misinterpret what is being said, i.e "analogous or equivalent" to being "equal". And even when you explain the difference between "equivalent" and "equal", they stubbornly refuse to acknowledge the analogy and usually they respond again with the phrase "No, they're totally different" and also may follow-up with another strawman. So I think it should be added. Usually it's not just poor communication or misunderstanting. It's either intentional, in which case it is a fallacious tactic or when it's unintentional that means it's a fallacy that confuses them, so why not include it? 

Thank you Rationalissimus of the Elenchus for bringing this up! I had never heard it, didn't know it had a name, but I've dealt with it many, many times from people who just wanted to continue to believe what they were believing and ignore the contradiction in their thinking. Just another tactic to hide their denial. 

Yeah, there's a genuine distinction between people who (unfortunately) don't get analogies, and those who see the logic but remain in denial.

As I like to say - "not every difference makes a difference". Two things being 'different' in a way does not mean they can't be compared at all.

Effectively; "perfect analogy" isn't always an independent fallacy - it's often an extension of the argument from fallacy, itself a form of fallacious reasoning.

Interesting analysis!