Dragon history can be summed up as follows: "The dragons of legend are strangely like actual creatures that have lived in the past. They are much like the great reptiles [dinosaurs], which inhabited the earth long before man is supposed to have appeared on earth." (Knox Wilson, "Dragon", The World Book Encyclopedia, Vol. 5, 1973, pg. 265.)
In light of that statement from The World Book Encyclopedia, many people don't realize that paleontology (the study of past geological ages based primarily on the study of fossils) is a relatively new science. In fact, the concept of dinosaurs (giant lizards) only surfaced in its present form less than 180 years ago. Prior to that, anyone who found a large fossilized bone assumed it came from an elephant, dragon or giant. There wasn't any notion of "science" attached to these finds.
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The Serpent Theory:
Many people believe that the origination of dragons came from serpents. Rather, they came from snakes and eels that people saw. As time went on and art evolved, these serpents became more and more decorated until they looked more like semi-Chinese dragons or sea serpents.
It is also suggested that people saw mutated eels and snakes or thought that some of their surroundings (i.e. for eels, seaweed, for snakes, sticks) were actually a part of them. Thus making them look as if they were draconic. This actually suggest that dragons were formed out of the misinterpretation of artwork, stories, and sights throughout the ages. Possible? Yes. It isn't as if they had cameras!
The Bones Theory:
This theory pertains to the remains that people found and called "dragon bones" so it definitely holds no water in battle of where the term dragon came from. However, it does provided an interesting idea that people thought the bones of dinosaurs to be dragons, and they though dragons to be descendants (or parents) to such serpents as the snake and lizard. The Bones Theory suggests that people found the bones and created stories about the fierce creatures that once lived within those bones.
Sadly, this theory is lacking when it comes to civilizations as China and other Asian dragons. Due to their unscientific structures, Chinese dragons and Asian dragons could never have originated from seeing bones. On the other hand, one might think that they either adapted the bones to the dragons or they only found some bones. Whichever the case, this theory is not as likely as the Serpent Theory.
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I believe dragons are possibly the reflection, sometimes embellished through retelling but mostly historical, of actual physical encounters of human beings with dinosaurs.
I am not at all convinced it has been proven that the dinosaurs became extinct prior to the advent of man. I believe there is much evidence, ancient and modern, to indicate that dinosaurs and humankind existed on earth contemporaneously, and that human beings, while they probably lived in different regions than dinosaurs for the most part, did on many occasions encounter the sometimes huge and fearsome creatures. The memories of these encounters were so vivid and deep that they were passed down in a multitude of cultures as legends, painted on cave walls, represented in pottery, and written of in literature.
Knox Wilson, "Dragon", The World Book Encyclopedia, Vol. 5, 1973, pg. 265
I wrote a report on dragons in college ;D