The English rather arrogantly insist that the game be called football, and all of us have probably acknowledged that the name is rather more apropos after all. Certainly it makes more sense than what we Americans call football.
The irony is that the English were the first to call the game soccer. While we were killing each other during our Civil War, the English were being far more productive, establishing the first official rules of football, and forming what came to be known as the Football Association.
Association football became a common term when it was necessary to distinguish it from rugby football.
Soccer is a colloquial abbreviation of association, derived from the second syllable of the word. Some believe it was first shortened to assoccer" and later to the simpler soccer.
This part is only legendary, but many have it that a certain schoolboy named Charles Wreford-Brown was asked by some Oxford friends to join them in a game of "rugger" (rugby). He supposedly replied that he'd prefer a game of soccer. The name stuck, and there you have it.
What's important to remember here is that soccer is not a crass Americanism. The word is part of the rich history of the game, and supposed aficionados who denounce it reveal only their own ignorance.