I have seen this term used frequently and I had never heard of it until a few months ago. I am wondering if most readers of general newspapers and magazines (where such a term is often used) are aware of its meaning and understand why it is called a quote-unquote "scare" quote.
Who ''coined'' the term “scare quotes”?
This appears to have originated amongst British logical philosophers in the late 1950s and early 1960s.
According to the Oxford English Dictionary, the earliest known use is from Mind 65 in 1956. Here it is with more context:
4 So nothing is or comes about by chance or ‘ whichever happens. ’ Nor will it be or not be, but everything of necessity and not ‘ whichever happens. ’ For either someone saying something or someone denying it will be right. For it would either be happening or not happening accordingly. For whichever happens is not more thus or not thus than it is going to be.
‘ whichever happens ’: the Greek phrase suggests both “ as it may be ” and “ as it turns out ”. “ As the case may be ” would have been a good translation if it could have stood as a subject of a sentence. The ‘ scare-quotes ’ are mine; Aristotle is not overtly discussing the expression “ whichever happens ”.
This is a paper by G.E.M. Anscombe (1919 – 2001) called “Aristotle and the Sea Battle”. Elizabeth Anscombe was a professor of philosophy at the University of Cambridge and collaborated with and was married to Peter Geach (born 1916).
Geach also used the term in Mental Acts: Their Content and Their Objects (1957) (reprinted 1971):
In contemporary logic there is a pretty general recognition of the rule that when we write down an expression for the purpose of talking about that very expression, we must show what we are doing by enclosing that expression within quotes; if this rule is not strictly observed, actual fallacies are likely to arise. Nothing in spoken language corresponds to this use of quotation-marks; the beginnings of the sentences "man is an animal" and " "man" is a noun" are phonetically quite alike. There is indeed a particular tone of voice that is conventionally represented by using quotes, as in "He introduced me to his 'wife' "; but such quotes (which are sometimes called "scare-quotes") are of course quite different from quotes used to show that we are talking about the expression they enclose. In this work I have tried to follow a strict rule of using single quotes as scare-quotes, and double quotes for when I am actually talking about the expressions quoted.1 I shall distinguish between a quotation and a quoted expression; the quoted expression is what stands between quotes, e.g. "man" in " "man" is a noun", whereas the quotation, " "man" ", in this case, consists of the quoted expression and the quotes.
1 There is very little practical risk of confusing the two uses of quotes, so reader may find this precaution rather like the White Knight's armouring his horse's legs against possible sharkbites. But once bitten, twice shy - I have actually been criticized in print for lack of 'rigour' because I used scare-quotes in a logical article without warning my readers that I was doing so.
Other early uses:
The Aristotelian Society's 1963 Supplementary Volume. I believe it was used in a paper called Symposium: Plato and the Third Man by Colin Strang and D. A. Rees, who acknowledge Geach (amongst others) and apparently Anscombe's name is on the following page.
Montgomery Furth in his 1964 introduction of his translation of Gottlob Frege's The Basic Laws of Arithmetic, and mentions Geach's translation of Frege on the same page.
From 1965 - 1970 some 20-odd other books, spreading from logical philosophy to ethics, theology, political and legal philosophy, political science, language and metaphysics, and to America and Australia.
Use continued in the 1980s but was on the whole restricted to these and related fields, and in the 1990s seems to have spread further within academia, but not much outside; the earliest news source I found using it was a 1994 Newsweek with other s using it once each in 1996, 1997 and 1998.
Why is the word scare used?
Because the writer is afraid to use the term directly, and places it instead in quote marks to attribute it to another.
For example, "This is a news website article about a scientific paper" from the Guardian:
In this paragraph I will state the main claim that the research makes, making appropriate use of "scare quotes" to ensure that it's clear that I have no opinion about this research whatsoever.
Edit: Dan Bloom has sourced a 1946:
It is impossible to find the first coiner of the term, but it happened long before 1946 when US writer Carey McWilliams used the term (with a hyphen: "scare-quotes") in a nonfiction book he was writing about California and Upton Sinclair's works.
The book by Carey McWilliams is Southern California: An Island on the Land and on page 298:
This edition is copyright 1946 and 1973 by McWilliams, but a search on Hathitrust appears to verify it in a 1946 edition.
FWIW (very little, I suspect), I studied a fair deal of epistemology in the mid-to-late-1980s, which is where I learnt the term and encountered an awful lot of actual usage of scare quotes. Anyway, I see no semantic relationship between the 1946 political advertising example and the scare quotes of mid-20th-century philosophy. The former seems quite clearly to be referring to a quite different thing: without having read the fuller context, in case it makes a difference to the interpretation, those "scare-quotes" seem to have been actual, presumably even literal, quotes from some politician or political operative that were specifically selected to scare voters away from casting a vote for a particular candidate in an election. So, whilst it is an earlier usage of the literal term, it is not the first usage of the term in the sense that the questioner was asking about. To be relevant to the question, someone would have to show some kind of linkage between that 1946 usage and the later, perhaps mid-20th-century philosophy, or at least academic, coinage. That said, very interesting that it has also been used in a more directly literal sense than in its (later) academic usage.
It's called a "scare quote" because it connotes that the quoted item is somehow "scary" - nonstandard, abnormal, different in a somewhat threatening way. Social activists might call it lexical Othering.
Oxford's definition is "quotation marks used around a word or phrase when they are not required, thereby eliciting attention or doubts." (https://google.com/search?q=scare+quotes).
A few years late for this question there was an article about them: https://www.theatlantic.com/entertainment/archive/2016/12/the-scare-quote-2016-in-a-punctuation-mark/511319/