Ambivalence over the name of the third season of the year reflects its status as a relatively new concept. As natural as it seems today, people haven't always thought of the year in terms of four seasons.
Fifteen hundred years ago, the Anglo-Saxons marked the passage of time with just one season: winter, a concept considered equivalent to hardship or adversity that metaphorically represented the year in its entirety. For example, in the Old English epic poem "Beowulf," the title character rescues a kingdom that had been terrorized by a monster for "12 winters."
According to "Folk Taxonomies in Early English" (Fairleigh Dickinson University Press, 2003) by Earl R. Anderson, the importance of winter in marking the passage of time is evidenced by the constancy of its name over time and across many languages. "Winter" probably derives from a root word meaning "wet" that traces back more than 5,000 years.
Summer is also a time-honored concept, though perhaps never quite as weighty a one as winter, and this is evidenced by greater ambivalence over its name. In Old English, the word "gear" connoted the warmer part of the year. This word gave way to the Germanic "sumer," which is related to the word for "half." Eventually, speakers of Middle English (the language used from the 11th to 15th centuries) conceived of the year in terms of halves: "sumer," the warm half, and "winter," the cold half. This two-season frame of reference dominated Western thinking as late as the 18th century. [What Causes Earth's Seasons?]
Incidentally, Chinese culture also had a two-season framework, but there, the major seasonal polarity was autumn (symbolizing adversity) and spring (symbolizing regeneration), with little importance given to the extremes of summer and winter.
In the West, the transitional seasons, being more trivial, were "not fully lexicalized in the language" until much later, Anderson wrote. Lexicalization is the realization of an idea in a single word.
In 12th- and 13th-century Middle English, spring was called "lent" or "lenten" (but this also meant the religious observance), and fall, when it was considered a season at all, was called "haerfest" (which also meant the act of taking in crops). In the 14th and 15th centuries, "lenten" gave way to a panoply of terms, including "spring," "spryngyng tyme," "ver" (Latin for "green"), "primetemps" (French for "new time"), as well as more complicated descriptive phrases. By the 17th century, "spring" had won out.
In terms of seasons, the period spanning the transition from summer to winter had the weakest credentials of all, and so it got lexicalized last. "Autumn," a Latin word, first appears in English in the late 14th century, and gradually gained on "harvest." In the 17th century, "fall" came into use, almost certainly as a poetic complement to "spring," and it competed with the other terms.
Finally, in the 18th century, "harvest" had lost its seasonal meaning altogether, and "fall" and "autumn" emerged as the two accepted names for the third season. But by the 19th century, "fall" had become an "Americanism": a word primarily used in the United States and one that was frowned upon by British lexicographers.
The persistence of two terms for the third season in the United States, while somewhat of a mystery, may have something to do with the spread of English to the American continent at the very epoch when "fall" began jockeying for position with "autumn": the 17th century. At that time, both terms were adopted stateside, and the younger, more poetic "fall" gained the upper hand. Back in Britain, however, "autumn" won out. The continued acceptance of "autumn" in the United States may reflect the influence, or at least the proximity, of English culture and literature.
According to Slate, British lexicographers begrudgingly admit that the United States got the better end of the stick. In "The King's English" (1908), H.W. Fowler wrote, "Fall is better on the merits than autumn, in every way: it is short, Saxon (like the other three season names), picturesque; it reveals its derivation to every one who uses it, not to the scholar only, like autumn."