Here are a couple of websites which can help explain the "armed" vs "unarmed" F-16 situation, and also give some insight as to how the day unfolded for the pilots who were scrambled (i.e., tasked to launch immediately).
In this first link, the section that begins "Down to Seven Bases" discusses the mission of Air National Guard (ANG) aircraft assigned to NORAD. As you can see from the article, this NORAD mission, readiness state, etc. is different from normal training missions on which other fighters were operating that day.
http://www.afa.org/magazine/Feb2002/...rad_print.html
The next link takes you to an article which was originally from
Aviation Week & Space Technology, and gives details about the aircraft, some of the pilots' perspectives, and the orders which came down the chain of command.
http://billstclair.com/911timeline/2...ogy090902.html
As a former F-16 pilot and Chief of Alert at a NORAD-assigned ANG unit, I can verify that (a few minor editorial misnomers notwithstanding), both articles have credibility and legitimacy.
My personal opinion? I believe AA717driver mostly has it right in his first sentence: "there were no armed aircraft around to do it." There
were armed aircraft, and all fighters eventually were authorized to use force, but none with armament ever got close enough to Flight 93 to be a factor. Just my 2p/2c worth, but it's by far the most logical answer in my view.