Argument from setting a precedent
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Argument from precedent is a common fallacy in discussion, for example on committees or in meetings. It consists in saying that to act correctly in circumstances X would be inadvisable, in case others consider that this would set a precedent for acting in circumstances Y, where (it is argued) X and Y are superficially similar but (on close examination) are radically different. See Microcosmographia Academica for the original statement.
The fallacy is similar to the slippery slope argument.