You can't carbon date a live oyster. A dead one maybe.
But seriously, accurate carbon dating can be done ONLY on organic matter that gets its carbon directly from the atmosphere. Carbon 14 is formed in the atmosphere from a relatively constant influx of cosmic rays. Terrestrial plants take up the carbon 14, terrestrial herbivores eat the plants, and terrestrial carnivores eat the herbivores, thus spreading the carbon 14 through all terrestrial life forms.
Sea life cannot be accurately carbon dated because sea water contains a high amount of ancient carbon in the form of carbonates that simple sea life forms take up, which are then eaten by larger life forms, and those life forms are eaten by larger life forms. That ancient carbon screws up the carbon 14 dating.
Creationist pseudo-scientists know that quite well but they are willing do do anything in their attempts to refute proper scientific findings, so they promote crap like carbon dating says a live oyster was 10,000 years old.