Read more on calibration and accuracy of radiocarbon dating.
To demonstrate that the rates of decay of unstable nuclei can be measured, that the exact time that a certain nucleus will decay cannot be predicted, and that it takes a very large number of nuclei to find the rate of decay.
It's not that the radioactive carbon in air or food doesn't decay, it does.
By about 58,000 years (ten half-lives) after an organism has died, there's so little radioactive carbon left (less than 1/1000) that calculations of age are no longer accurate.
That's why radiocarbon dating is only reliable for samples up to 50,000 years old.
So the proportion of carbon-14 inside living things is the same as the proportion of carbon-14 in the atmosphere at that time.
But when we stop eating, or when plants stop photosynthesising, our carbon-14 levels no longer get topped up.
When those speedy protons hit atoms you end up with a few stray neutrons zipping around the place.