The Fallacy of Accident was one of Aristotle's orginal Fourteen. It is a simple fallacy: Confusing a generalization, or "rule of thumb", with a universal generality. The term "accident" refers to the formal logic definition of the term: "A circumstance or attribute that is not essential to the nature of something, " like the color of a cow. That is, an irrelevant or incidental detail.
All the cows around here seem to be brown. This animal is brown. This animal must be a cow.
These might seem easy to identify and to deal with, but sometimes they are subtle, and sometimes people get hung up on the words, instead of the sense of the thing. We live by Rules of Thumb, and they serve us well. That's the problem, on rare occasions. Sometimes, keeping the generalization unspoken (when many might object to the generalization if it were overt) adds to the effect:
"Katrina proved Bush wants to kill blacks." This is a near-psychotic generalization in which an implied (hostile, and a total lie) generalization - "Bush hates Blacks" - is put to partisan use to exploit bad weather, employing the Accident Fallacy to alienate black voters in the future.
"Books are meant to be read." True statement but an obnoxious, obesssional type might object to the fallacy in it. Art books are to be looked at, not read. In this simple case, the exceptions are overlooked. We call that "poetic license."
"This murder case has all of the earmarks of the Boston Strangler, so we must redouble our efforts to find this evil demon." More complex here, because the rule of thumb breaks down in the face of "copycat" criminals, a common phenomenon amongst the non-creative bad guys who no doubt were not permitted enough time to finger-paint in nursery school.
"Moslems seem sensitive to the cause of the Jihadists, because their silence communicates support." Here we have a generalizing assertion with a non-trivial fallacy embedded in it. What if a majority of Brit and US Moslems feel intimidated by the Mullahs? They may be cowardly, but not supportive, like many Germans during the Nazi era. Or they may be quietly supportive. Who knows?
Thus there are more subtle forms in which Accident can insinuate itself into writing, and into our brains, without alerting itself with a sign. Our own brains must provide the signs before we are lead down the primrose path to illogicality. Therefore always watch out for the unstated generalizations, or assumptions, which are concealed in an assertion.