I am just wondering.
Everyone seems fixated on the western idea of a dragon being identical, so let me be the first to toss that idea out of the window. There are multiple kinds of Chinese dragon, including some resembling the western, but the two most important I would say would be the imperial dragon, and what we would call dinosaurs. So, in fact, when dinosaur bones are discovered, they use the word dragon for this. As a result, there is plenty of evidence dragons existed, just walk into your local dinosaur museum and you'll see the word plastered all over the exhibits.
Here is one such modern example: http://www.cnn.com/2015/01/30/asia/china-dragon-dinosaur/
Here the farmers who excavated the dinosaur bones deemed it, 'Qijianglong', which we in the west term mamenchisaurid, a type of dinosaur endemic of China. This is only an example, many other 'dragons' have their origin in dinosaur bones.
They can be forgiven for calling this a dragon.
The second, and more legendary kind, is the imperial dragon that represents the emperor. This creature is featured both as a symbol of state power and one of the primordial animals that aids the creation of the earth. It is found as early as Neoithic times and is often the subject of ancient jade and bronze works.
By being immaterial and heavenly, the dragon symbol overrides all other animals in its divinity, just as the emperor overrides all people. Some emperors were even said to bear a birthmark like this to signify imperial destiny, and this was at times necessary when dynasties changed hands and the imperial dragon's features would change with it, mainly centering around red, blue and especially yellow dragons.
There were even clothing restrictions that said only the emperor may wear a robe of nine dragons, and wearing such a thing usually represented a pretense to become a pretender to the Mandate of Heaven, the Chinese idea of a divine right of kings. Until the Chinese Revolution when the Qing Dynasty fell, an imperial dragon was on the flag of China. This was then replaced by Sun Yat Sen's five colors representing the five races of China, Chiang Kai Shek's twelve pointed star in a blue field on red representing capitalist China, and finally the flag of Communist China, the five stars on a red field.
So you see, there is a very real origin of this creature. Dinosaurs, and a convenient symbol of state power.
It's only mythological if you don't believe it exists. The Chinese zodiac is filled with creatures that were believed to exist. It's all a matter of perspective.
edited to correct typo: "were"