This paper investigates collective neutrino-antineutrino oscillations in dense neutrino environments. The authors argue that for massless neutrinos, collective oscillations between neutrinos and antineutrinos are suppressed due to helicity suppression. The amplitude for the backward scattering process $ \nu_{p_{1}}\overline{\nu}_{p_{2}}\rightarrow\nu_{p_{2}}\overline{\nu}_{p_{1}} $ vanishes for massless neutrinos, implying no off-diagonal refractive index between $ \nu $ and $ \overline{\nu} $ of a single flavor. For non-zero neutrino masses, collective helicity oscillations are possible, representing $ \nu-\overline{\nu} $ oscillations in the Majorana case. However, these phenomena are suppressed by the smallness of neutrino masses. The paper discusses the possibility of collective neutrino-antineutrino oscillations in dense neutrino environments, highlighting the role of off-diagonal refraction. It shows that for a coherent superposition of neutrinos and antineutrinos, a refractive effect can occur, leading to flavor conversion. However, for massless neutrinos, the amplitude for the backward scattering process vanishes, preventing such oscillations. The paper also addresses the difference between neutrino-antineutrino scattering and neutrino-neutrino scattering, showing that the former has a vanishing amplitude due to helicity conservation. The authors conclude that collective neutrino-antineutrino oscillations cannot occur for massless neutrinos due to helicity suppression, and that the amplitude for the backward scattering process vanishes. This conclusion is in contrast to previous work by Sawyer, who suggested that such oscillations could occur. The paper also discusses the implications of these findings for neutrino physics, including the possibility of flavor conversion in dense neutrino environments.This paper investigates collective neutrino-antineutrino oscillations in dense neutrino environments. The authors argue that for massless neutrinos, collective oscillations between neutrinos and antineutrinos are suppressed due to helicity suppression. The amplitude for the backward scattering process $ \nu_{p_{1}}\overline{\nu}_{p_{2}}\rightarrow\nu_{p_{2}}\overline{\nu}_{p_{1}} $ vanishes for massless neutrinos, implying no off-diagonal refractive index between $ \nu $ and $ \overline{\nu} $ of a single flavor. For non-zero neutrino masses, collective helicity oscillations are possible, representing $ \nu-\overline{\nu} $ oscillations in the Majorana case. However, these phenomena are suppressed by the smallness of neutrino masses. The paper discusses the possibility of collective neutrino-antineutrino oscillations in dense neutrino environments, highlighting the role of off-diagonal refraction. It shows that for a coherent superposition of neutrinos and antineutrinos, a refractive effect can occur, leading to flavor conversion. However, for massless neutrinos, the amplitude for the backward scattering process vanishes, preventing such oscillations. The paper also addresses the difference between neutrino-antineutrino scattering and neutrino-neutrino scattering, showing that the former has a vanishing amplitude due to helicity conservation. The authors conclude that collective neutrino-antineutrino oscillations cannot occur for massless neutrinos due to helicity suppression, and that the amplitude for the backward scattering process vanishes. This conclusion is in contrast to previous work by Sawyer, who suggested that such oscillations could occur. The paper also discusses the implications of these findings for neutrino physics, including the possibility of flavor conversion in dense neutrino environments.