Caution: This may be a very naive question but I find it confusing. Moreover, I believe this question is based on potential misconception. I would like it to be clarified.
Although the neutrinos are electrically neutral and colorless they have non-zero weak hypercharge $Y=-1$ (for left-chiral neutrinos), and lepton number $L=1$. So how can the possibility that neutrino being its own antiparticle be entertained? Even if we assign $L=0$, there is still the non-zero hypercharge fixed by the relation $Y=2(Q-I_3)$. So why can't we surely tell that there are antineutrinos, distinct from neutrinos, and charecterized by $Y=+1$?
If we assign, $L=+1$ for right-handed sterile neutrinos $N_R$, can I any longer entertain the possibility that $(N_R)^c$ to be same as $N_R$?
As far as I know, photons are their own antiparticles, that is clear. But particle physicists are not sure whether neutrinos are self-conjugate or not. They often treat neutrinos are Majorana particles and often as Dirac particles. Why is this ambiguity not there for photons?