Fallacy of Accident

The logical fallacy of accident, also called destroying the exception or a dicto simpliciter ad dictum secundum quid, is a deductive fallacy occurring in statistical syllogisms (an argument based on a generalization) when an exception to the generalization is ignored. It is one of the thirteen fallacies originally identified by Aristotle. The fallacy occurs when one attempts to apply a general rule to an irrelevant situation.
For instance:

Cutting people with a knife is a crime.
Surgeons cut people with knives.
Surgeons are criminals.

It is easy to construct fallacious arguments by applying general statements to specific incidents that are obviously exceptions.
Generalizations that are weak generally have more exceptions (the number of exceptions to the generalization need not be a minority of cases) and vice versa.
This fallacy may occur when we confuse generalizations ("some") for categorical statements ("always and everywhere"). It may be encouraged when no qualifying words like "some", "many", "rarely" etc. are used to mark the generalization.
For example:

Germans are Nazis

The premise above could be used in an argument concluding that all Germans or current Germans should be held responsible for the actions of the Nazis. Qualifying the first term:

Some Germans are Nazis

This premise may make it more obvious it is making an (extremely weak) generalization and not a categorical rule.
Related inductive fallacies include: overwhelming exception, hasty generalization. See faulty generalization.
The opposing kind of dicto simpliciter fallacy is the converse accident.

No true scotsman fallacy!

No true Scotsman is a logical fallacy where the meaning of a term is redefined to make a desired assertion about it true. It is a type of self-sealing argument. The term was advanced by philosopher Antony Flew in his 1975 book Thinking About Thinking: Do I sincerely want to be right?.

Imagine Hamish McDonald, a Scotsman, sitting down with his Glasgow Morning Herald and seeing an article about how the "Brighton Sex Maniac Strikes Again." Hamish is shocked and declares that "No Scotsman would do such a thing." The next day he sits down to read his Glasgow Morning Herald again and this time finds an article about an Aberdeen man whose brutal actions make the Brighton sex maniac seem almost gentlemanly. This fact shows that Hamish was wrong in his opinion but is he going to admit this? Not likely. This time he says, "No true Scotsman would do such a thing."
—Antony Flew , Thinking About Thinking (1975)
A simpler rendition often given follows:

Teacher: All Scotsmen enjoy haggis.

Student: But my Scottish uncle Scotty McScottscott doesn't like haggis!

Teacher: Well, all true Scotsmen like haggis.

This is an ad hoc attempt to retain an unreasoned assertion. When faced with a counterexample to a universal claim, rather than denying the counterexample or rejecting the original universal claim, this fallacy is employed to shift the definition of the original class to tautologically exclude the specific case or others like it.
A universal claim is of the form "All x are y" or "No x are y." In the example above, the universal claim is "No Scotsmen are brutal maniacal rapists." The counterexample is given by the Aberdonian, who, it is implied, is a brutal maniacal rapist. The response relies on a continued insistence that No Scots are brutal maniacal rapists, and to thus conclude that the brutal maniacal and rapacious Aberdonian is no true Scot. Such a conclusion requires shifting the presumed definition of "Scotsman" to exclude all brutal maniacal rapists.
In situations where the subject's status is previously determined by specific behaviors, the "no true" construction is not a fallacy of this kind. For example, it is perfectly justified to say, "No true vegetarian eats meat," because not eating meat is the single thing that precisely defines a person as a vegetarian. In this phrase the qualifier "true" is a comparison to, e.g., "a pretending vegetarian".