Why It's Called Football
Some might say, simply, "because they kick the football."
But the real story is deeper. The origin of American football is in the history of the world's most popular sport: soccer. When soccer -- more universally known as "football" (which of course makes sense because soccer players use their feet) -- players decided to change their centuries-old game with restrictions such as the no-use-of- hand rules, people who disliked this broke away to create rugby. In the states we have created our own version of the game under the same old name "football" with more of a rugby style, the whole time forgetting why we call it that.
Here are other answers:
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 football didn't used to allow the "forward pass" and much more of the play involved foot work, 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 "rouge" when the kicker is able to kick the ball thru the end zone, so it lands out of play , it is worth 2 points. 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 "rouge" is worth a single point here in Canada.