Almost from the start of aviation we've seen quite a huge number of weird contraptions, all in search of a better way to fly.
German engineers came up with so many weird designs that the few that did warrant further investigation and development lead to the idea that everything they touched turned into gold. Disk like flying objects had been tried over the years and with the introduction of the jet engine and increased speeds the classic understanding of aerodynamics went out the window and people once again came up with radical new ideas in the hope to find something that would stick.
In a time where planes went increasingly higher and faster and certain phenomena were not really well understood, there were increased claims of strange sightings.
Although we were in the middle of the red scare, the default attitude was to assume that the Soviets were technically backwards and incapable of matching the technology of the West as was shown by the need to prop up the USSR in WWII, but with access to German research combined with their own work, the Soviets showed several times they were quite ahead, with designs like the Mig 15, Sputnik, SA-2 Guideline and others.
So while some did believe the Soviets were hardly a threat, others feared that the Soviets might come up with a radical breakthrough that would render current weapons obsolete. So while some did claim that the Soviets couldn't produce jets capable of the speeds UFO's allegedly were capable of, people who had some knowledge of projects like the X-15 or the SR-71 feared the Soviets might have something and the Air Force organized think tanks to figure out how such a craft would be possible. This is the Cold War and paranoia had people grasping at straws, CIA and FBI were more than willing to listen and meticulously record anyone who had a special claim, just in case they happened to know something useful.
Ever since WWII there has been a mountain of literature that favours a rather spectacular view of German secret weapon development, most of them claiming that if the war had gone on for a little while more, the Allies would have been devastated by super-advanced secret weapons that were so sophisticated they were beyond everything the Germans had produced before and wouldn't suffer all the problems and glitches that had plagued German weapon development and production up to that point.
And for some reason, they always come to the conclusion that it's either nazi hyper-technology or aliens, never a lie, a mistake or wrong conclusions from people who don't know what they saw. And every cook and crazy loon who wasted somebody's time at the FBI or CIA is now seen as proof that the intelligence agencies were collecting vast amounts of data and know exactly what's going on.
It's only logical that the military would look into the problem, just in case it might be a threat to national security. Hollywood and everyone who ever wrote a book to make a buck off the stupid has only helped to fuel the idea it's a huge conspiracy …
