  In this note, we discuss the pathological nature of black holes in
Einsteinian Cubic gravity and its extensions. We compute the equations for the
odd perturbations and show how spherically symmetric solutions that
asymptotically approach a maximally symmetric space (Minkowski, de Sitter or
anti-de Sitter) are associated to having an asymptotically degenerate principal
part of the equations. We use these results to argue that the encountered
problems will be generic for any other cubic or higher-order with a reduced
linear spectrum around maximally symmetric spaces except the well-known healthy
case of $f(R)$. We highlight that these pathologies are only alarming when the
theory is regarded as a complete theory, but not when considered as a
perturbative correction to GR (as in e.g. the effective field theory framework)
since the the low-energy physics remains safe from them. Our results thus cast
doubts on possible resolutions of the singularities or non-perturbative effects
on horizons based on these theories.
