Supercritical carbon dioxide (scCO(2)) on its own can be a relatively poor solvent. However, the addition at relatively modest concentration of "entrainers", simple solvent molecules such as ethanol or acetone, can provide a significant boost in solubility, thereby enabling its industrial use. However, how entrainers work is still under debate; without an unambiguous explanation, it is hard to optimize entrainers for any specific solute. This paper demonstrates that a fundamental, assumption-free statistical thermodynamic theory, the Kirkwood-Buff (KB) theory, can provide an unambiguous explanation of the entrainer effect through an analysis of published experimental data. The KB theory shows that a strong solute entrainer interaction accounts for the solubility enhancement, while CO, density increase and/or CO2-entrainer interactions, which have been assumed widely in the literature, do not account for solubilization. This conclusion, despite the limited completeness of available data, is demonstrably robust; this can be shown by an order-of-magnitude analysis based upon the theory, and can be demonstrated directly through a public-domain "app", which has been developed to implement the theory.