In-depth discussions and controversies about the trope and real-life issues related to it should go here, rather than the main page, so as to avoid natter.
Controversy surrounding the Wright Brothers' claim:
Even if the description of the Wrights' "first heavier-than-air flight" is refined to 'manned and powered' heavier-than-air flight, it still leaves much room for debate. Suffice to say that many people and groups of people tried many different things and the lines between actual flight, gliding and short hops were not always clear. The Wrights may in fact only be able to claim having the first extensively recorded example of the narrowed category above... but that is also debated.
The reason the Wrights are so widely attributed credit for being the first is because they are the first known to build a piloted, heavier-than-air machine, that was capable of controllable flight. The key element here being that the pilot could control and maneuver the plane.
Another thing that favors the Wright's claim is that they extensively documented their work, including considerable photography. The evolution of their designs from glider to powered flight is clearly evident from their records. Wilbur Wright's correspondence with the Smithsonian Institution and the U.S. Weather Bureau (which led to the selection of Kitty Hawk, NC for their experiments because of its consistent winds) is also a matter pf public record. Even if there was any doubt about their flight at Kitty Hawk in 1903, they also flew on multiple occasions at Huffman Prairie near Dayton, OH in 1904 (flying for up to five minutes at a time, including complete circles) and 1905 (flying up to 38 minutes at a time). These flights were witnessed and reported by journalists.
While the Wright Brothers' twelve second flight is the most famous, they actually made four flights that day, with the longest lasting a full 59 seconds. While the first "flight" may be debatable, the last one certainly counted as a controlled flight. They had also refined their design to be practical by 1905 (practical here meaning that it flew until fuel ran out. Meanwhile, Santos-Dumont, who made the first flight in Europe (and who is sometimes mistakenly referred to as the "true father of flight"), did not fly until 1906.
Supporters of Santos-Dumont often claim that the Wright brothers' first flight was assisted by a catapult that propelled the plane at take-off (while Santos-Dumont's plane took off on its own power), but this is probably not true: The Wrights used catapults for their later demonstration flights, but insisted that their first flight was taken under its own power. However, supporters of Santos-Dumont still point that the first Wright flight was assisted by a headwindnote A headwind is only a disqualifying advantage if the airplane lands behind where it took off. If the airplane lands in front of where it took off, it is capable of flying under its own power, and the headwind just served to shorten the length of runway needed, while Santos-Dumont's first flight was not; Santos-Dumont's flights were also better documented, and had more witnesses. It is also claimed that Santos-Dumont's plane was more practical, and better anticipated later aircraft, because it had a wheeled undercarriage, while the Wrights used skids and rails on their plane; the Wrights explicitly believed that their design was the more practical one, but turned out to be mistaken in the long run.
The Wrights' original Flyer was not an astonishing or unexpected innovation in itself: very many were attempting more or less the same thing, and once a sufficiently light and strong engine was available someone was going to get up in the air. The brothers deserve more recognition for their scientic approach to solve the problem reliably and efficiently. They used wind tunnel technology (fairly widely used in Europe but almost unknown in USA) to work out the design of the wings. They also worked out the basics of three-axis control (invented by them) before even attempting to take off. This is in contrast to some of their contemporaries who seem to have had simply dreamed up something vaguely flying-machine-like and then pushed it off a roof to make it fly.