I'm not sure that the comparison between the difficulty of breaking the sound barrier and the difficulty of breaking light speed works all that well.
In the case of the sound barrier, it was probably pretty obvious that it could be broken - after all, every time anyone fires a gun, the bullet pops out and does that immediately. The German V2 - the first large rocket - also did that all the time. If you just want to fly faster than sound, no problem. You just shape your vehicle correctly (the front of the X-1, the first supersonic aircraft, was designed around the shape of a rifle bullet, just scaled up a bit) and stick in a power plant capable of overcoming the drag. The big problem was in controlling a manned aircraft. That's where people really had problems, especially with the controls effectively locking up at near-sonic speeds. The X-1 only succeeded when someone had the idea of the all-moving tailplane. Basically, until then virtually all aircraft used conventional elevators i.e. only a small part of the rear wing was used to control the aircraft's pitch (how high up the nose was). Making the whole rear wing move instead was the final piece of the puzzle for manned, controlled, supersonic flight.
With faster-than-light travel, we do not even know how to fire something out of a gun in an essentially uncontrolled fashion at FTL speeds. It's a basic difficulty in physics, not in engineering. As others have noted in this thread, in its current state our physics tells us that it is in principle impossible. All the ways around it that I know of involve doing weird things to spacetime and still moving locally at less than light speed, such as using wormholes or a type of "bubble" spacetime (Alcubierre spacetime?) inspired by Star Trek warp-drives - and there are still basic theoretical difficulties with even those ideas that would need to be solved before we can even begin to think how to actually turn them into an engineering problem.
Another thing to keep in mind in any UFO discussion is even undoubtedly experienced observers can make errors. For instance, there are occasions on which experienced airline pilots have swerved violently to avoid a collision with a bright meteor over 100 miles from their position. And my favourite identification error is from Richard Rhodes' "The Making Of The Atomic Bomb", in which he relates an incident that occurred just weeks before the testing of the first atomic bomb. Early one morning the anti-aircraft gun crews at Los Alamos saw a bright unidentified object in the dawn sky and opened fire when it would not identify itself. The base commander, who was also an amateur astronomer, sent out a request for the gun crews to stop trying to shoot down the planet Venus. Still, there certainly are odd things that it would be interesting to know the explanation for.
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