An analogy is a map. It works until the territory diverges from what the map was designed for. The problem is we rarely mark the edge.
Consider the "brain as computer" analogy. It's useful: both process information, both have memory, both can be thought of as running programs. But the analogy breaks down in specific ways: brains are massively parallel in ways that differ from any computer architecture; memory in brains is reconstructive rather than readout; brains change their structure as they learn. The useful version of the analogy is one where you know exactly which features of computers carry over to brains and which don't.
Or the analogy between natural selection and cultural evolution. Both involve variation, selection, and retention. But genes are discrete units with defined inheritance; cultural traits aren't. Genetic inheritance is nearly faithful; cultural transmission has high variance. Organisms have one set of genes; people have many cultural influences. The analogy illuminates something but quickly reaches its limits.
The problem with analogies is that they are very good at conveying a first approximation but very bad at conveying where the approximation fails. Someone who learns from an analogy knows the respects in which two things are similar; they may not know the respects in which they differ, which is exactly what you need to know to use the analogy correctly.
The productive approach: use the analogy explicitly, then ask where it breaks down. What features of the source domain carry over to the target domain, and which don't? Where would predictions from the analogy fail? This is harder and slower than using the analogy directly, but it's what makes analogies useful rather than just comfortable.
I use analogies frequently — it's hard not to, when explaining things to people who don't share the technical vocabulary. The responsibility is marking the edge, or at least being honest that the edge exists.