Carbon dating is probably correct up to a point of about 3,500 to 4,000 years ago. What I understand about the evolutionary position is the assumption is made that the world has been pretty much stable since it came into existence billions of years ago, (uniformatarianism). The creationists position is the world came into existence about 6,000 years ago and about 4,000 years ago there was a world wide flood that affected the amount of carbon in the atmosphere and the pre-flood forests could have diluted the buildup of carbon. (catastrophism) We don't know what the carbon was like right after the beginning of the world.
Below is a picture that helps explain the controversy. The red line is the assumption by evolutionists and the blue line is the assumption by creationists.
“It is obvious that radiometric techniques may not be the absolute dating methods that they are claimed to be. Age estimates on a given geological stratum by different radiometric methods are often quite different (sometimes by hundreds of millions of years). There is no absolutely reliable long-term radiological ‘clock.’ ” William D. Stansfield, Science of Evolution (New York: Macmillan Publishing Co., 1977), p. 84.
This is ludicrous. Please explain the means by which the concentration of Carbon-12 in the atmosphere affects the atomic rate of decay in Carbon 14.
FYI, the reason C-14 is only reliable for a few thousand years is that the atomic rate of decay is relatively quick, with a half-life of 5730 years. If it were not constantly replenished by means that are well understood, there wouldn't be any of it left to test.
That's why we ALSO depend on Rubidium-87, Rhenium-187, Thorium-232, Uranium-238, Potassium-40, Uranium-235, Samarium-147, Iodine-129, and Aluminum-26, with half-lives ranging from 740,000 to 49,000,000,000 years.
Even if you manage to find evidence that carbon decayed at a different rate before "the flood" (which would require a fundamental re-write of the laws of physics), you still have the 36 OTHER unstable isotopes scientists use to establish the age of the earth and date geological and fossil evidence to deal with.
All of them agree.
None of them support your cherished creation myth.
Please wake up to the earth you're living on, for all our sakes.