  It has been claimed that cosmic censorship conjecture can be violated by
quantum tunnelling of neutrinos, though it is strongly supported by classical
arguments. We consider the classical interaction of an extremal Kerr black hole
with a test massless Dirac field, i.e. a "neutrino field". Evaluating the flux
integrals imposed by the energy momentum tensor for fermionic fields and the
Killing vectors of the space-time, we prove that this interaction can indeed
destroy the event horizon of the black hole and convert it to a naked
singularity. The classical process leads to a more generic violation of cosmic
censorship conjecture compared to quantum tunnelling processes which occur with
a low probability. The range of frequencies of the test neutrino field that can
be used to destroy the black hole turns out to be the superradiant range for
bosonic fields. We comment on back reaction and quantum effects. We argue that
the destruction of black holes by neutrino fields cannot be fixed by self-force
effects unlike similar attempts involving test bodies and bosonic fields.
