Although what Americans call "soccer" and the rest of the world calls "football" consists of almost all players using their feet to play the game, Americans decided to use the name ''football'' for another sport (What other countries call American Football). Some feel that this is incorrect and that the sport doesn't fit the name since probably 90-95% of the time the "football" doesn't touch any of the players feet. But it should be understood by all that there are no rules or laws of the world saying that a sport must be called by a name that the majority of the world uses, and it should also be understood that although the ball might not "touch" a players foot for most of the game, feet are being used for much of the game, including running, kicking, and scoring.

For example, to get the ball to the other end of the field and to the goal a player must run, stumble, hop, and trample among other things to get over and through the opposing sides teammates. No matter how much passing (or throwing as some would call it) is involved, there has been no known game where passes were thrown through the entire duration of the game and not anyone had to use their feet at all to gain progress. It is basically impossible to throw the whole distance of the football field through the entire game to gain points (for both teams). There has also been no known game where, again, through an entire duration players floated, hovered, crawled, walked on their hands or did anything of the sort to gain progress and to gain each and every point. They had/have to use their feet no matter which way they are trying to score. Although there is passing, sometimes it is misconstrued by those who don't completely understand the sport, that that isn't all there is (There is also a thing called the ''run game'').

So, although Americans may not have gone with what seemed to be the easier and more popular route of naming the two sports (soccer=football, football=pass ball, or throw ball, or catch ball to some) that does not mean it is wrong, or that it doesn't make sense, or that the name should be changed because it doesn't fit in with the entire world.
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It's a reflection of the game's origins. The first football-type games played on U.S. college campuses were kicking-oriented sports like soccer. But every school had its own rules. It wasn't until the 1870s that the schools convened to agree on a standardized set of rules -- which, at Harvard's prodding, were based on the English rugby code. Rugby, of course, is really "rugby football." And since everyone had already been calling it football, the name stuck -- although it could just as easily at that point have become known as American rugby.

Kicking was a much more prominent part of the game in the early days than it is now, too. Before the forward pass was legalized, teams attempted more field goals, and punting was considered a primary defensive strategy for a team whose running game was bogging down.

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The word 'football' is from the English language and was originally spelled as 'foot ball'. When the term 'foot ball' was first used in medieval England it described 'a ball game played on foot' known as mob football or Shrovetide football in which more running with the ball was required than kicking the ball. These ball games had earlier descriptions such as 'playing at ball' and there were similar if not identical ball games being played in other countries at the same time. These games include 'Hurling' played in Wales & Cornwall and 'La Soule' or 'Choule' played in the north of France. However, mob football or Shrovetide football was the first ball game to be specifically referred to as 'foot ball'. I have created the link 'Shrovetide football' from the BBC which provides an insight into how the game is played showing photos of the Up'ards and Down'ards 'mob' playing the game.

These Shrovetide games evolved into other forms of football notably Rugby football which was said to have been started by a pupil at Rugby school called William Webb Ellis in 1823. The Rugby Union Football world cup is called the "Webb Ellis Trophy" after him. The rules of early Rugby contributed too many other codes of football in England and other English speaking countries during the 19th centaury. American football is one of these games. It could be argued that American football is a purer form of football than say Association football (soccer) or Australian Rules football because like Rugby is retains more of the original medieval characteristics.
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Some might say, simply, "because they kick the football." But the real story is deeper. The origin of Gridiron (American football) is in the history of the world's most popular sport: Football (soccer). When soccer -- more universally known as "football" (which of course makes sense because football players use their feet) -- players decided to change their centuries-old game with restrictions such as the no-use-of-hands rules, people who disliked this broke away to create rugby. The US version of the game under the same old name "football" (Gridiron) has more of a rugby style, the whole time forgetting why it was called that.

* Gridiron (American football) is a derivative of rugby football, and while the feet are used more often in rugby than on the gridiron, much of the game is still played by handling the ball. Both variations are still considered football.
* North America style Gridiron (American football) did not originally use the "forward pass" and much more of the play involved footwork, such as the "drop kick" and the running punt kick. In the first rules, only the " side pass" was allowed, as long as the two players were side by side, with no forward motion of the ball, similar to rugby rules. The Canadian Football League ( CFL ) still allows a drop kick to score a field goal, and also has a thing called a "safety" when the kicker is able to kick the ball through the end zone, so it lands out of play. Both the NFL and the CFL still have the drop-kick available as a weapon - on the point-after-touchdown, or from the field for 3 points. The "safety" is worth a single point in Canada. The Canadian game also features the ability, on fumbles, to kick the ball, but not on incomplete passes. It also features a 'touch back' which is a tackle in the end-zone, which is worth two points (called a safety in US football
* The global name for football (soccer) is of course football. The global name for American football is Gridiron. Gridiron is a type of handball and not football. Football is a sport where players control the ball with their feet and only football (soccer) does this. Gridiron is where hands are used to control a ball. Football has been played for many centuries but had no official rules. The British created rules for football in 1848. After that many codes of handball arose including rugger and gridiron, none of which are codes of football.
* It's a reflection of American football's origins. The first football type of game that colleges played in North America was almost identical to what became soccer: You scored by kicking a goal. But every school had its own rules. That was true even over in England, before the Football Association was created to establish a standard set of rules. Over here in the USA, we had no such governing body, so the schools took it upon themselves to sit down and draw up their own set of rules that everyone could agree on.

In an age when overseas communications took weeks, if not months, Americans lived in relative isolation from their football counterparts in Europe and thus weren't able to easily keep tabs on how the game was progressing there. So Americans (and Canadians) took it upon themselves to sort things out on their own and draw up a set of rules that appealed to them. Although most schools in North America were playing some variety of soccer, others, including Harvard, preferred a game that was more like rugby. When the schools first met to discuss a set of rules, Harvard pressed to base their common rules on the English rugby code, and they prevailed. From that point on, the American version of football began to develop out of rugby instead of soccer.
The same process of codifying rules had happened in England, too: After the Football Association was formed, some clubs disagreed over which rules to use -- primarily, the rule that governed the use of hands in the game. Those who favored prohibiting the hands formed the Football Association, and those who wanted to use the hands as part of the game eventually went on to form the first Rugby Football Union.

The American game could just as easily have been called American rugby, but since everyone was already calling it "football," the name stuck. Besides, in the early days, the American game was much more kicking-oriented than it is now. When there was no forward pass and kicks could be taken from anywhere on the field, teams would frequently dropkick to try to score, or they'd use a deep punt as a defensive strategy, if their running game was getting bogged down. It was only when the forward pass was legalized and kicks were limited to those taken from behind the line of scrimmage that the feet began to play a less prominent role in the American game. But again, everyone already called the game football, so there was no reason to change it.

Just keep in mind that what we call "rugby" is actually "rugby football," yet rugby players handle the ball as much as they kick it. What most of the world calls simply "football" is technically "association football," from the name of its founding and governing body. When soccer and rugby split, the association game simply adopted "football" as its name, while rugby football focused on the first part of its name. That doesn't mean one game is football while the other isn't. They're still both football games with a shared origin.
What's more, since the soccer/rugby split, other football-related games have evolved to emphasize other parts of the body to propel the ball. In fact, of the world's six major football codes -- soccer, rugby league, rugby union, Australian rules football, American (gridiron) football, and Gaelic football -- soccer is the only one that prohibits use of the hands. And they all employ kicking strategies to a greater or lesser extent.

In 1895 Rugby football clubs north of England based in Huddersfield, Yorkshire created a break-way game that became known as Rugby League Football. This is a faster game with 13 players instead of the 15 as used in the Rugby Union game. In Britain today a football club will typically carry the name of the village, town or city in which the club is located followed by one of three acronyms namely AFC (Association Football Club), RUFC (Rugby Union Football Club) or RLFC (Rugby League Football Club). All are considered forms of football that evolved from a common game with very few rules which can be traced hundreds of years. As American football was created by emigrants influenced by these games American Football shares these common origin as do the people whose medieval European ancestors who played the game in its original primitive pre-codified form.