Creationist claims carbon dating
They do it because they know that if the earth is more than 6,000-10,000 years old, it's absolutely game over for young-earth creationism and biblical literalism in general.They lie, twist and misrepresent the facts about radiometric dating (and wholly ignore the many other corroborating methods) that tell us the actual age of organic materials to preserve their foundational fantasy at all costs.You'd expect to find 100 grams of element A in a sample if it was brand new.If you find 50 grams, the sample must be about 250 years old.
Note that this limit of accuracy (which only applies to radiocarbon dating of all the radiometric dating methods) is still ten times longer than the time span required to comprehensively debunk young earth creationism.
All radioactive substances have these half-lives, and we know them to a pretty good precision.
Obviously once you get very little of a substance (after about ~10 half lives, IIRC) it's not very useful for dating materials, but as I said, there are a lot of them and their useful periods overlap, so we have a lot of ways to check our numbers.
But to answer WHY they do it, it's because they have to.
they have already committed to an explanation "god did it", and if they don't deny key facts about biology, astronomy, geology, chemistry etc then they can't continue to reinforce the belief that they are right, and they can't benefit from the comfort that belief gives them.
When an organism dies, it ceases to take in new carbon-14, and the existing isotope decays with a characteristic half-life (5730 years).