That flight United flight 93 was taken down by the military, but not with an air to air missile - instead with advanced weaponry using electromagnetic interference.

“documentation abounds showing that the Air Force and the Pentagon have conducted extensive research on "electronic warfare applications" with the possible capacity intentionally to disrupt the mechanisms of an aeroplane in such a way as to provoke, for example, an uncontrollable dive. Scarry also reports that US Customs aircraft are already equipped with such weaponry; as are some C-130 Air Force transport planes. The FBI has stated that, apart from the enigmatic Falcon business jet, there was a C-130 military cargo plane within 25 miles of the passenger jet when it crashed”

https://www.independent.co.uk/news/world/americas/unanswered-questions-mystery-flight-93-173206.html