"As my mom told me, a cop is like a cheetah in pack of gazelles. It's going to catch the slowest one it can!" ... said someone I knew once, explaining why the last slowest offender will be the one to get the ticket. That makes sense, except for the part where that's totally not what would happen. The analogy breaks down because the cop's motivation is not the same as the cheetahs. However, if someone misses this, they will leverage the analogy to make the wrong conclusion.
Why even have an analogy at all? Analogies are a transformation to a familiar set of concepts that are similar enough to drive home the point. This can be useful for very abstract ideas (electricity, theoretical physics, ... ) but really it's best to just talk about what the topic really is. There's no opportunity for creating a distorted frame of reference, and usually it's not a big deal to just talk about the actual concepts. In fact, if you get an analogy perfectly right, you're really just calling things by different names!
I think people like to spout off analogies to show off how deeply they understand a topic, ironically, each subtly wrong analogy shows their lack of detailed understanding of the original topic.
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