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False Equivalence Fallacy
A False Equivalence, or False analogy is an informal fallacy applying to inductive arguments. A false analogy consists of an error in the substance of an argument (the content of the analogy itself), not necessarily an error in the logical structure of the argument. For example, in suggesting two things are equally bad, no judgment is made that either thing may not be bad, but the comparison between the two as being equivalent is highly questionable.
In an analogy, two systems are shown to have common sub-functions and/or properties and therefore additional corresponding sub-functions and/or properties are proposed and shown to exist. This is repeated for all sub-functions until the analogy ultimately fails.
More specifically the assumption of an analogy runs like this: if some system A has some function X and also some function Y, and some system B has a function X′ corresponding to A's function X, then the system B should also have a function Y′ that is analogous to A's function Y.
For instance, a popular analogy is between plumbing and electrical circuits. In plumbing there are sub-functions and properties such as valves and fluid flow rate. These functions and properties have corresponding analogs in electronics such as transistors and electrical current.
Another analogy concerns the gravitational force between two masses and the electrical force between two charges (both are governed by inverse square relations). One might be tempted to create a further analogy between plumbing and the gravitational force. It is difficult to say whether this would be a false analogy since the definition of a true analogy is equally difficult to define. The usefulness of any analogy must lie in the number of analogs it can establish between the functions and properties of two systems.
An example of a false analogy between energy and mass would be to assume that since E=mc2, then energy and mass must be identical. Energy and mass are not identical, energy can travel at the speed of light while mass cannot. Analogies should never be mistaken for establishing an equivalence. Not recognizing the misapplication of analogy can be as potentially disastrous as not recognizing a misapplication of logic.
Incorrectly classifying an analogy false
Very often people try to refute a correct analogy as a false analogy, often saying "Well, but that's different because", and refer to an existing property that the two things in the analogy indeed do not share. In cases like this, such a refutation is merely a "false charge of fallacy". But as analogies are comparing two different things there are always some properties that A and B do not share, so it is tempting to pull up one such difference to try to disqualify the analogy. For the purposes of the analogy, however, it is important to check if that difference is relevant for the analogy or not.
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