Rumour has it "football" was originally a term for games "played on foot". Some people liked to played a kicking variation while others liked a carrying variation. Both soccer and rugby were called "football".
Makes you wonder what sort of world people lived in where games played on foot were enough of a minority to require a specific term. What sports aren't played on foot? Polo, auto racing, ice hockey, wheelchair sports. That's all I can think of. Isn't cricket played "on foot"? Didn't it already exist when football was invented?
Though the best argument to make is simple. American football gets to be "football" because America runs the world and Europe doesn't. I'm not even an American but I know that's how it works. So kick/dive-ball is "soccer" because America says it is.