The paper discusses the possibility of collective neutrino-antineutrino oscillations in dense neutrino environments, a concept recently advanced by Sawyer. The authors argue that while flavor oscillations can occur due to a flavor off-diagonal refractive effect in a gas of coherent superpositions of different flavors, the same effect does not apply to neutrinos and antineutrinos of the same flavor. They provide a detailed analysis of the helicity structure of the forward scattering process, showing that the amplitude for backward scattering ($\nu_{\mathrm{p}} \bar{\nu}_{\mathrm{p}} \rightarrow \nu_{\mathrm{p}} \bar{\nu}_{\mathrm{p}}$) vanishes for massless neutrinos, and is suppressed for non-zero neutrino masses. This implies that there is no off-diagonal refractive index between neutrinos and antineutrinos of the same flavor, and thus, no collective neutrino-antineutrino oscillations can occur. The authors conclude that the rate of collective neutrino-antineutrino oscillations must always vanish with vanishing neutrino mass, contrasting Sawyer's earlier findings.The paper discusses the possibility of collective neutrino-antineutrino oscillations in dense neutrino environments, a concept recently advanced by Sawyer. The authors argue that while flavor oscillations can occur due to a flavor off-diagonal refractive effect in a gas of coherent superpositions of different flavors, the same effect does not apply to neutrinos and antineutrinos of the same flavor. They provide a detailed analysis of the helicity structure of the forward scattering process, showing that the amplitude for backward scattering ($\nu_{\mathrm{p}} \bar{\nu}_{\mathrm{p}} \rightarrow \nu_{\mathrm{p}} \bar{\nu}_{\mathrm{p}}$) vanishes for massless neutrinos, and is suppressed for non-zero neutrino masses. This implies that there is no off-diagonal refractive index between neutrinos and antineutrinos of the same flavor, and thus, no collective neutrino-antineutrino oscillations can occur. The authors conclude that the rate of collective neutrino-antineutrino oscillations must always vanish with vanishing neutrino mass, contrasting Sawyer's earlier findings.