http://wiki.answers.com/Q/Why_is_American_football_called_%27football%27 (
http://wiki.answers.com/Q/Why_is_American_football_called_%27football%27)
Read that. Thou shalt be enlightened.
As to the no thinking aspect, lol. That's what people who have never played football.
The whole team has to remember what certain wording means, for instance on defense "4-3 cover 3 will" would mean line up in a 4 linemen, 3 linebacker, 3 corner back formation with 1 safety. And the will would signify that the will (weak) linebacker is blitzing his/her gap (a gap is the space between offensive linemen and each gap is named with a letter. On offense, however, gaps are normally referred to as holes and have numbers assigned to them for the running back to run through). "4-3 cover 3 ton", however, could mean that the nose tackle and other defensive tackle switch positions after the start, one cutting across and the other moving in a loop. And those are SIMPLE plays. Plays that are run in *middle school* football.
Players need to understand 100s of key words to understand what's happening on a given play, and quarterbacks additionally need to know the signs for each of those words so he and the coach can communicate.
And in some plays, decision making happens after the snap too. For instance, there are some plays known as a triple option, where the quarterback first must read the defense instantly and decide whether or not to hand it to the running back. If he doesn't, he then runs through a hole or a sweep with another running back beside him, forcing the defense to go after him. He then must choose to pitch to the running back or keep it himself. And on passing plays, the quarterback must decide who to throw to (and those receivers must memorize routes based on numbers; 5 could mean a 5 yard hitch route, and 7 may mean a 10 yard post).
All that's just scratching the surface.
Football is much more complicated for players to learn than people think. Oh, and since it's such a fast paced game, they need to make all their decisions in milliseconds, and one person making the wrong one can be the difference between a 2 yard loss and a 20 yard gain.
Yeah. I seriously went there.