  We show that the common singularities present in generic modified gravity
models governed by actions of the type $S=\int d^4x \sqrt{-g}f(R,\phi,X)$, with
$X= -{1/2}g^{ab}\partial_a\phi\partial_b\phi$, are essentially the same
anisotropic instabilities associated to the hypersurface $F(\phi)=0$ in the
case of a non-minimal coupling of the type $F(\phi)R$, enlightening the
physical origin of such singularities that typically arise in rather complex
and cumbersome inhomogeneous perturbation analyses. We show, moreover, that
such anisotropic instabilities typically give rise to dynamically unavoidable
singularities, precluding completely the possibility of having physically
viable models for which the hypersurface $\frac{\partial f}{\partial R}=0$
exists. Some examples are explicitly discussed.
