Carbon-14 dating does give ages that are incompatible with a literal interpretation of the Bible. The question, then, is whether or not Carbon-14 is giving us valid data.
There are quite a few assumptions used in Carbon-14 dating:
- The rate of C-14 decay (half-life) has always been the same.
- The C-14/C-12 ratio in the Biosphere (equilibrium) has remained constant.
- The specimen was in equilibrium with the Biosphere when buried.
- The specimen had not gained any carbon since it was buried.
- Today, we can measure the correct C-14/C-12 ratio in the specimen.
If any of these assumptions is invalid, then the dates we get from Carbon-14 dating would be inaccurate and completely irrelevant to the discussion. Any reasonable person should admit this. The onus is then on those who accept all of the assumptions as true without proof.
As it turns out, there is evidence that the rate of decay has not always been constant, and there is also evidence that the C-14/C-12 ratio is still not in equilibrium. So, if that's the case, Carbon-14 dates should be considered inadmissible in the court as evidence.
Propounding the difficulties is the fact that when multiple dating methods are used on the same specimen, wildly different results are found. For instance, if the Carbon-14 test gives a date of 50,000 years, but the Uranium-Lead test gives 100,000 years, and the Potassium-Argon test gives 200,000 years, the question is often asked which one is accurate. Yet, why should we say any of them are accurate with such extreme inconsistency? Even if the 100,000 year date fits into what was expected, it doesn't mean it's correct. If all the dating methods consistently returned results within 1-3% of each other, that would be significant, but that is not the case at all.
If a professor gave a specimen to his students to date, and he used one method and each of the students used a different method, the professor would give each of them an "F" on the assignment, because they would differ that much from the result the professor himself got.
So, creationists just simply respond to the Carbon-14 evidence with a request for proof that all of the assumptions used are actually true, and we also ask for an explanation of why multiple dating methods disagree so much with each other.
Then, we would probably point to some of the many evidences for creationism, such as the earth's decreasing magnetic field, the departing moon, the presence of meteorites, the continued rotation of the earth, the 2nd law of thermodynamics... and a million other things. In any discussion on such things, the evolutionist and creationist should both split their time defending and presenting evidence. Too many times creationists are forced into only countering so-called evidence for evolution, and the evolutionist never has to answer anything.
So, that's how a creationist would answer such evidence.