if y'all want the genuine reason why we call the sport here 'football', it's the same reason why - in addition to the 'football' most people internationally think when they hear the term - you also got aussie rules football, gaelic football, and rugby football.
they all descended from various types of 'football' that were played at english universities in the 18th century (yes, i am aware that there have been sports called 'football' dating back centuries, but this is when they started to codify actual rules and jive for the sport)
like you look up what's considered the first american football game ever (an 1869 game between princeton and rutgers), the rules they used for the game were based on the football association's 1863 rules - which are now the codified rules for soccer (hence why it's also called 'association football'), so if you got a time machine and watched the game, you'd think it was just soccer and not american football.
but eventually universities and stuff started to instead base their rules off of rugby (still a code of football) and that eventually became the standard base on which american football rules evolved from and became its own sport rather than just a variation on rugby. (ever wonder why the sport has 'touchdowns' despite there being no touching down involved? it's because we adapted the concept from the rules of rugby, where the analogous concept is known as a 'try', which does require you to ground the ball in the opponent's goal area - and you had to do that in the early years of rugby-based american football as well. it's also why you have the thing where the team that scored tries to get an extra point by kicking the ball through the goal posts - that's the whole reason why it was called a 'try' in rugby, it was a 'try at goal'. you got the ball into the opponent's goal area and touched it onto the ground? your team got a chance at getting a goal and scoring a point, basically)