Bivalve farming was usually considered as a CO2 source through respiration and calcification, but recent studies suggest its potential as a CO2 sink, prompting exploration of its inclusion in carbon markets. Here we reviewed the scientific basis behind this idea and found that it is not supported by observational and experimental studies. This idea indeed arises from carbon budget models that are based on theoretical misconceptions regarding seawater carbonate chemistry. The main misunderstanding consists of assuming that the carbon trapped in the shell originates from atmospheric CO2 when it mostly comes from (bi)carbonate ions. While these ions originate from atmospheric CO2 through the erosion of minerals over geological time scales, their incorporation into shells does not prompt short-term CO2 compensation. The opposite occurs—calcification releases CO2 in seawater and limits or even prevents the uptake of atmospheric CO2. Some authors suggest that considering the bivalve farm ecosystem could change the perspective on the source/sink issue but there is no evidence for that now. Most ecosystem-based carbon budget models rely on several unverified assumptions and estimates. Although challenging, field measurements must be conducted for monitoring, reporting, and verifying atmospheric CO2 uptake before qualifying for carbon credits. To achieve scientific consensus, we need reinforcing measurement-based studies of CO2 fluxes in shellfish ecosystems, integrating carbon balance models with observational and experimental science, and fostering interdisciplinary collaboration. Although bivalve farming provides numerous environmental benefits and is vital for sustainable aquaculture, there is currently no evidence that it contributes to CO2 capture.