The answer to this question lies in what carbon-14 dating is and how it works.
From HowStuffWorks.com: “Carbon-14 dating is a way of determining the age of certain archaeological artifacts of a biological origin up to about 50,000 years old. It is used in dating things such as bone, cloth, wood and plant fibers that were created in the relatively recent past by human activities.”
(full article explaining the dating process here…)
Due to the half-life of the carbon-14 atom, we are only able to accurately date an object up to about 60,000 years. We do not refute it as evidence that the Earth is millions of years old because it is not capable of making that kind of claim. If there are people out there that due use this argument, they don’t understand what they are talking about and need to do some more research.