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Reportedly, the man who stands at the origin of the word soccer is Charles Wreford Brown, an Oxford student who always preferred shortened versions of words, such as brekkers for breakfast, or rugger for rugby.
Soccer gained popularity in the United States later than in the rest of Europe and since the Americans already had a use for the world "football" in understanding the sport of American Football, a middle option was tried on in between 1945 and 1975, when the organization that controlled soccer in the USA was called the "United States Soccer Football Association".
Besides being long, the name was still confusing so after 1974 it simply adopted the name of "United States Soccer Federation" and the word "soccer" would define the sport in the US area ever since.
It's often mistakenly thought that the United States are the only country that uses the term soccer for what is traditionally known as football in Europe, Asia and other parts of the World. However, the new name was adopted by other countries, specifically those that associated football to a different sport prior to soccer being popular. Such countries include Australia, Canada, New Zealand and some parts of Ireland.