My friend Rachel asked me this question recently. Great topic for another blog post. Here goes:
The Bible tells us that God created dinosaurs and all other creatures on Day 6 of creation week (which really was a "day" per the 4th commandment, my condolences to Old Earth apologists!)
We know that when Adam and Eve fell, all creation fell under the curse (Romans 8:19,21). Now that death entered the universe, many animals apparently became carnivores, including some dinosaurs, see Did Animals Eat Meat Before the Flood. The first "Climate Change" took place, putting dinosaurs at a great disadvantage because of their huge size. Most probably men and dinosaurs migrated in different directions, because of the climate and the fear induced by dinosaurs.
The massive changes brought by the global flood of Noah's day ultimately took out the Dinosaurs (a minority opinion is held by Klenk, who says they died out before the Flood because of the dinosaur's affinity with evil, see Genesis and the Demise of the Dinosaurs) If any remained afterward, they were extremely few and far between. The Behemoth of the Job 40:15-24 may have been one of those leftovers, see Dinosaurs and Humans Coexisted.
All this would explain the mysterious but contemporary-sounding quality of all the ancient "dragon" stories that have been passed down to us.
One thing about dinosaurs/dragons. The fear and fascination they universally induce should point everyone to their need for a savior. And the only one who can truly save is Jesus, that's for certain. He says "Fear not, I have redeemed you, I have called you by name, you are mine." (Isaiah 43:1b)
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