Everyone in the military (including the Air Force) scratches their heads over why ridiculous and over-sized swords are given to high ranking Air Force officers. The real reason is rooted in tradition and a dash of silliness. U.S. Air Force NCOs honor officers who have made significant contributions to the enlisted corps by inducting them into the Order of the Sword. The keeper of the Air Force Master Sword, the Chief Master Sgt. of the Air Force, bestows the honored officers with a sword of their own, fitting to their duty.
According to the Air Force's claim: "The original order of the sword was patterned after two orders of chivalry founded during the Middle Ages in Europe: the (British) Royal Order of the Sword and the Swedish Military Order of the Sword, still in existence today. In 1522, King Gustavus I of Sweden ordered the noblemen commissioned by him to appoint officers to serve him, and these people became known as the non-commissioned officers."
Eagle-eyed historians would poke holes in many of those claims. The Brits don't have an Order of the Sword. The Sweds didn't have one until 1748, which is way later than what is considered the Middle Ages — and they haven't inducted anyone since 1975. The Romans already had a form of an NCO, France's King Charles VII helped form corporals a century earlier than Gustavus I, and Baron Von Steuben helped finalize the American NCO Corps as we know it with the "Blue Book" for the Colonial Army, so, yeah, there are some holes in this origin story.
As for the current Air Force Order of the Sword, the inductee is chosen by the enlisted airmen on a strictly confidential matter. Having roughly 50,000 airmen keeping a secret is nearly impossible, so the decision is made by the 15 senior most enlisted. Because of this, seven consecutive 4-star commanders of the United States Air Forces in Europe were placed into the order.
But it's the design of sword that draws the most attention. The over-the-top pageantry that goes into the design is a source of entertainment and jest all around the military.