So, what did the controller mean by their thinking it must be a military pilot? That the plane was desending at a higher forward speed than any commercial pilot would, and was in fact doing a much greater speed than any commercial pilot would be doing while approaching the ground. Commercial aircraft simply do not do low level at high speed, it frightens the passengers and shakes the plane up. Only fighters do that, thus the statement that this looked like a fighter manouver.
It was also turning to do what would look somewhat like an approach to National airport yet any commercial pilot would have gone much further out and reduced speed while turning and desending. A landing approach at that speed is also unsafe for a large commercial jet. Fighters often land faster than civilian aircraft.
However it must be kept in mind that Hanjour had nothing "safe" in mind for the aircraft or the souls on board. Low level unsafe flight? Sure, why not, after all one must fly low and fast if one's intent is to crash the plane and do maximum damage. Turn and desend at high forward speed? Sure, why not if one is intent on getting the aircraft to slam into a building as soon as possible. Hanjour never did anything that was technically particularily difficult. He did not even concern himself with such tasks as dropping the landing gear or extending flaps. He did many things that a pilot intent on staying alive and well and keeping his aircraft and passengers intact would not do, but those were not a concern to Hanjour.
