Because the time it takes to convert biological materials to fossil fuels is substantially longer than the time it takes for its in the atmosphere, which attained a maximum in 1963 of almost twice what it had been before the testing began.
Measurement of radiocarbon was originally done by beta-counting devices, which counted the amount of beta radiation emitted by decaying atoms in the sample and not just the few that happen to decay during the measurements; it can therefore be used with much smaller samples (as small as individual plant seeds), and gives results much more quickly.
To verify the accuracy of the method, several artefacts that were datable by other techniques were tested; the results of the testing were in reasonable agreement with the true ages of the objects.
Over time, however, discrepancies began to appear between the known chronology for the oldest Egyptian dynasties and the radiocarbon dates of Egyptian artefacts.
For consistency with these early papers, and to avoid the risk of a double correction for the incorrect half-life, radiocarbon ages are still calculated using the incorrect half-life value.