False Analogy
A false analogy treats one shared feature as if it were enough to make two cases explanatory twins. The trap is not comparison itself. Comparison is useful. The trap is sliding from "these look alike in one respect" to "therefore they must work alike in the respect that matters."
This fallacy usually appears when similarity substitutes for mechanism. Ancient and modern warming both involve rising temperatures, but that does not tell you whether they have the same cause. Two illnesses can both produce fever without coming from the same infection. Two businesses can both grow quickly without being driven by the same economics. The right question is always: is the similarity relevant to the conclusion being drawn, or is it just rhetorically convenient?
The fastest test for a false analogy is to ask what important differences have been ignored. If the conclusion collapses as soon as context, mechanism, or scale is restored, the comparison was doing more work than it deserved.
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See also: critical-thinking-and-logical-fallacies for how this fallacy fits alongside the full pattern of argument failures.