The Flintstones

Are dinosaurs a problem for Bible-believing Christians?

i) There are many examples of now-extinct animals which were contemporaneous with man in the past. Several Ice Age animals are familiar examples, viz. wooly mammoth, mastodon, saber-tooth tiger, cave bear, Irish elk, dire wolf. 

There are various conjectures on why they went extinct, viz., climate change, overhunting by humans. 

One might ask how humans could drive T-Rex into extinction. Well, I can't say for a fact. But certain scenarios come to mind. They could kill it by setting a wildfire: it burns to death. Or by using torches to scare it off a cliff. Or by setting an underground animal trap, where whatever falls in will be impaled on sharp wooden stakes.

Human hunters can be very ingenuous. In brain v. brawn, brainpower usually wins–if given enough lead-time to make necessary preparations. 

But there's also the climate change explanation. 

ii) Apropos (i), on a YEC chronology, dinosaurs were contemporaneous with man. However, if man originated in Mesopotamia, the fact that men and dinosaurs occupied the same period doesn't mean they occupied the same place. If man stayed in the Mideast before the flood, he might have had little or no occasion to encounter a dinosaur. Depends on their respective ranges.

I'm not making a claim one way or the other. I'm not qualified to say. Rather, I'm saying we often come to the issue with unexamined assumptions. So biogeography is one of the questions we need to take into account. Assuming YEC is true, did men and dinosaurs have overlapping ranges? 

Assuming a global flood, all would have perished in the flood except for juvenile pairs taken aboard the ark. But they were unable to survive in the postdiluvial world.

iii) On an OEC chronology, God introduced dinosaurs by fiat creation into the world long before he made man, and they went extinct long before man. So that's not a problem for OEC, both because OEC espouses a local flood, and in any case the survival of dinosaurs would be moot since, on OEC chronology, they were already extinct long before the flood.