In order to understand why Carbon-14 (often written as 14C) dating gives erroneously ancient dates, we must understand both how Carbon-14 dating works and the assumptions used for interpreting the results.
Cosmic rays are constantly streaming into earth’s upper atmosphere. When one of these high energy particles hits an air molecule, neutrons can be released which then react with 14N to form 14C. This atom rapidly reacts with oxygen to form a 14CO2 molecule. Plants take in the 14CO2, animals eat the plants, and the net result is the uniform dispersion of radioactive carbon throughout the biosphere (all living organisms) in the same ratio that it is found in the atmosphere. The current ratio of radioactive 14C to normal 12C is 1 atom of 14C to 1 trillion (a thousand billion) atoms of 12C. As long as any organism is alive, it continues to take in both 14C and 12C in this ratio. But as soon as the organism dies, the radioactive 14C begins to decay without being replenished, so the ratio of 14C to 12C decreases. It takes 5730 years for 1/2 of the original 14C to decay. Thus, if something has a 14C to 12C ratio of 1 to 2 trillion, instead of the current 1 to 1 trillion, it is thought to be 5730 years old. A ratio of 1 to 4 trillion would be interpreted as 11,460 years old, 1 to 8 trillion would be 17,190 years old, etc. At a ratio of approximately 1 to 423 trillion, the amount of 14C is essentially unmeasurable and the organism is assumed to be older than 50,000 years.
This widely used dating method assumes the ratio of 14C to 12C in living things has been practically constant throughout the measurement period. Yet it is a fact that this ratio is not constant but has increased measurably from the time of the ancient Egyptian civilization until today. Artifacts from this ancient culture have to be corrected for a known increase in the ratio, but how can we assume that we know it was changing at the same rate before this historical time period? The method is corrected for this non-equilibrium, but the obvious implication (that a major disturbance could have radically changed the 14C to 12C ratio) is seldom considered. The world-wide flood as described in the Bible would have been such a disturbance.
During this worldwide flood, enormous quantities of plants and animals would have been buried, and massive amounts of carbon dioxide would have precipitated out of the oceans as calcium carbonate. After this event, the world rapidly readjusted, but the total carbon in the biosphere and oceans would have been much less than before the flood. Thus, if the generation rate of 14C was constant before and after this flood, then the ratio of 14C to 12C would have been much smaller before the flood than it is today. Thus, the assumption of a uniform 14C to 12C ratio throughout the measurement period is erroneous and cause vastly overstated ages for those organisms alive before and immediately following this flood.
The bottom line is that you cannot accept both the reality of a worldwide flood and accept radiocarbon dates of greater age than the date of this flood. The flood would have caused an enormous shift in the Carbon-14 level of all creatures. Many scientists believe this flood happened within the last 5000 years, making any artifact radiocarbon dated older than this invalid. Such an artifact simply contains a lower concentration of Carbon-14, because at the time it was alive, the available Carbon-14 was spread throughout more living organisms. Organisms alive shortly after the flood would be dated ten of thousands of years old (using current assumptions) even while they were still alive!