Answer

May grace be yours and peace in Christ Jesus.

Well, first of all, we would not use the word “rationalize,” which implies defending a false position with some countervailing facts. We would rather say that such matters can be explained, scientifically and biblically.

Secondly, there are dinosaurs around today—alligators, caimans, komodo dragons and such are modern-day dinosaurs.

Thirdly, I don’t really see your point. I don’t know anyone in our church who denies the existence of dinosaurs, or saber-toothed tigers, or other extinct species. They once lived on the earth and are now extinct.

Apart from all of this, carbon-14 dating has nothing to do with dinosaurs. Carbon-14 dating is only valid, at most, to 20,000 years, which is within human history. For example, the National Center for Science Education, which bills itself as “Defending the Teaching of Evolution and Climate Change,” says in one article,

Radiocarbon dating doesn't work well on objects much older than twenty thousand years, because such objects have so little C-14 left that their beta radiation is swamped out by the background radiation of cosmic rays and potassium-40 (K-40) decay.” (http://ncse.com/cej/3/2/answers-to-creationist-attacks-carbon-14-dating)

Having said all this, perhaps you have questions about the belief that the world was made out of nothing in the space of six days. And yes, this we believe, as we read in the Westminster Confession of Faith, Chapter 4, paragraph 1,

It pleased God the Father, Son, and Holy Ghost, for the manifestation of the glory of his eternal power, wisdom, and goodness, in the beginning, to create, or make of nothing, the world, and all things therein whether visible or invisible, in the space of six days; and all very good.

In doing so, we reject the myth of evolution, and all that it implies. This reflects the biblical teaching where God says to us in Hebrews 11:3, “By faith we understand that the worlds were framed by the word of God, so that the things which are seen were not made of things which are visible.”

I could go point by point and show how the biblical facts of creation are scientific and supported by scientific discoveries and theories, unlike the myth of evolution. But, you asked a limited question, and, hopefully, this is the beginning of an answer. There is, of course, much more that can be said.

May the Lord bless you in his grace, now and forever.