By analogy with another type of football, i.e. rugby football which was nicknamed rugger in the old days. Soccer was always a nickname, and association football the formal name.
The term "football" was used in medieval England to refer to sports played on foot as opposed to on horseback. There was a class element too as football games (of which there were many types) were played by the common man while equestrian sports were the realm of the elites. There were even laws passed regulating how much "football" could be played so it wouldn't distract from other peasant responsibilities.
