As an adjective, the word coed, short for coeducational, indicates an institution that teaches both males and females. However, as a noun, it can only mean "a young woman who attends college". Why is this so and how did this come about?
Cornell University, one of the first universities to embrace coeducation, became a coed institution in 1870. In a 2005 book by Margaret A. Lowe titled Looking Good: College Women and Body Image, 1875-1930, the author explains using first-hand accounts by the pioneering "coeds" of the time:
But once intertwined with feminist politics (whether embraced or disavowed on campus), coeducation further threatened Cornell's decision to admit women. The feminist link painted female students with the derogatory brush of unladylike desire. Considered strident intruders, they took the heat for destabilizing gender categories—it was they who crossed into male space and therefore put their moral authority in doubt. Female students would be called "coeds"; the term "student" referred solely to men. One early Cornellian recalled, "We were called 'co-eds'...and we should have been much more touchy than we were to mind it." In a humorous column for the Cornell Era, another student recalled that on her first day in Ithaca, "a boarding house keeper, of British birth, asked me if I were a a 'co-hed.'...'Co-head'!...But the attitude of our British friend was not so far remote from that of out student brother; to both a coed (A co-head) is an anomaly, a monstrosity."
In other words, the males were called students while the females were not; they were instead called coeds. So, the sexism theory prevails.
Webster's estimated date of first use—1878—is in keeping with the above excerpt. Etymonline's estimate is off by a couple of decades. There are a few other sources that also cover this topic; but all they do is parrot the (correct) dictionary definition rather than provide any real insight into the why and how of the question.
The process is called metonymy, calling the members of a set something associated with that set. A student of a type of educational system is called by the name of the system.
But this doesn't explain why only females are called by this term. Even though logically both males and females in a co-educational environment could be called 'co-eds', only females were. At the time of adoption of this word (the late 19th c), most colleges were predominately male, and for the college to become 'co-educational' the newer students who were also much fewer in number, were the females. Since the newer set is the exceptional case, the metonymy only applied to the marked case, the females.
The formal explanation: "The process is called metonymy, calling the members of a set something associated with that set. A student of a type of educational system is called by the name of the system." makes a lot of sense.
... as in atheletes: jocks, drive-in waitresses: car-hops, contract workers: temps, prisoners: cons, US soldiers: GIs, adolescents: teens, etc.
It is of no significance that the use of the word "coed" to identify a woman was at times defamatory, hip, sexy, or neutral. What is stated here is a verifiable answer for how female students came to be called coeds.