(I have to say, though, that part of me feels sorry for the confusion I certainly cause students who, no doubt trying simply to finish some assignment, type in the words "what is the fallacy of false analogy" and end up landing on a post in which I argue that it's not even clear that there is any such thing. I doubt it makes things easier for them.)
I've picked on Wikipedia a number of times -- not from any Wikipedia hate, but simply because its struggles to say anything even remotely coherent on the subject always end up summing the actual incoherence of the folklore on this topic. I went by the false analogy article recently and noticed that they cleaned it up a lot. But they're still struggling. Here's their current example:
A further clear example is:
Sam: "I think that people can have some affection for their cultural heritage."
Michelle: "You're just like Hitler!"
In the above example, Michelle has evaded a reasoned discussion by tarring Sam with an irrelevant association to an idea that Hitler used. Of course no one person is identical to another to the extent that their proposals can be disparaged by a mere reference to that other person. It is a form of ad hominem: Attacking the messenger, rather than the message.
Not so clear, I think; not only do we have cross-contamination from a completely different fallacy, but it has the "just like" shift, whose status is unclear, and it's not clear that we are dealing with analogy rather than just classification according to common features (although, admittedly, depending on one's theory of classification those two might be interrelated). This particular explanation is interesting in one respect, in that the explanation makes the false analogy a fallacy of irrelevance. In general, though, fallacies of irrelevance involve a shift in meaning, due to equivocation, or due to a mismatch between means and ends, neither of which are clearly involved here. Conceivably there could be some other kind of fallacy of irrelevance, but the mention of ad hominem suggests that the irrelevance is practical, due to a mismatch of means and ends. We don't know, however, any of the context, so we don't know what the ends are here. They could be stipulated, but then the example is not a clear example.
Wikipedia is not the only place that has a problem. I just noticed that onegoodmove.org has in its discussion of false analogy:
In an analogy, two objects (or events), A and B are shown to be similar. Then it is argued that since A has property P, so also B must have property P. An analogy fails when the two objects, A and B, are different in a way which affects whether they both have property P.
This doesn't work, however. The major problem is that it's simply not necessary to analogy that there be a shared property P at all. It is entirely possible, and arguably much more common, to say that since A and B are very much alike, and since A has property P, B must have a P-like property Q, i.e., where you are simply matching properties without making any claim about what they have in common. Analogical arguments don't necessarily require that they have the very same property, even when we are talking only about obviously reasonable analogical inferences. They allow a little mutatis mutandis. But if this is so, then the characterization of false analogy is not going to work.