When the game was codified, i.e., people sat around, wrote a rule book and created leagues, the sport we know of was officially named Association Football. This is why so many national organizations that choose to use football also have the word Association in their title. And since the game was codified in England, English fans have called the game football.
Why then does the United States use soccer? When Association Football made it to the US, rugby was undergoing experimentation that would later birth American Football. So, the term football was already in use. However, soccer was being used as a slang term for association football. (Ruby was often called rugger, so this isn't totally nuts.) Naturally, using this colloquialism as the primary name for the sport made more sense than having two football sports.