We know that in the Standard Model (SM) neutrinos are massless. But the discovery of neutrino oscillation suggests that neutrinos must have masses because only then there will be a mass basis for neutrinos and neutrinos will mix among each other through the PMNS matrix $U_\text{PMNS}$. Now my question is:
Couldn't we explain the neutrino oscillation through the Flavor Changing Neutral Currents (FCNC) or some other Beyond-SM phenomena so that neutrinos remain massless?