  We construct thought experiments involving the perturbations of Kerr-Newman
black holes by neutral test fields to evaluate the validity of the weak form of
the cosmic censorship conjecture. We first show that neglecting backreaction
effects, extremal Kerr-Newman black holes which satisfy the condition
$(J^2/M^4)<(1/3)$ can be overspun by scalar fields. This result, which could
not be discerned in the previous analyses to first order, is prone to be fixed
by employing backreaction effects. However the perturbation of Kerr-Newman
black holes by neutrino fields leads to a generic overspinning of the black
hole due to the absence of a lower limit for the frequency of the incident wave
to ensure that it is absorbed by the black hole. For this case, the destruction
of the event horizon cannot be fixed by any form of backreaction effects. This
result should not be interpreted as a counter-example to any of the previous
results which were based on the assumption that the null energy condition is
satisfied. We clarify and justify our arguments with numerical examples.
