it's not set in stone but historians tend to agree that football is called football, not because you kick the ball with your foot but, because it's played 'on foot' (as opposed to, say, on horseback). the nobs played on horses. the commoners played on foot.
in the 19th century, there was a more formalised split into association football (shortened to 'assoc' then morphed into 'soccer') and rugby football (played primarily by carrying the ball with the hands). both were considered football.
american colleges picked both these games up later and continued to call them football. the american game evolved into something different - especially with the introduction of the forward pass - but the name stuck.
simple
alasdair