Harpaston
Football, rugby, and soccer are believed to have descended from the ancient Greek game of harpaston. Classical literature often mentions Harpaston as a very rough and brutal game. The rules of this sport were quite simple: Points were awarded when a player would cross a goal line by either kicking the ball, running with it across the goal line, or throwing it across the line to another player. Whichever team was defending their goal, had to stop the offense any way possible. There was no specific field length, no side line boundaries, no specified number of players per team, and a huge lack of rules. Because of the lack of rules many injuries occurred. imagine going out and playing a mixture of football, rugby, and soccer but with the ability to body check anyone with the ball.
England's kings at the time outlawed football because it took popularity away from the previously popular sport, archery. Because of this football split into soccer and rugby. Eventually these three sports were played at separate English schools, people would go to a school that was specifically good at the sport o choice. Once American football was created it was totally unthinkable that these three sports had anything in common.