  Inflation can be parameterized by means of truncated flow equations. In this
"horizon-flow" setup, generic results have been obtained, such as typical
values for $r/(1-n_\mathrm{S})$. They are sometimes referred to as intrinsic
features of inflation itself. In this paper we first show that the
phenomenological class of inflationary potentials sampled by horizon-flow is
directly responsible for such predictions. They are therefore anything but
generic. Furthermore, the horizon-flow setup is shown to rely on trajectories
in phase space that differ from the slow-roll. For a given potential, we
demonstrate that this renders horizon-flow blind to entire relevant
inflationary regimes, for which the horizon-flow trajectory is shown to be
unstable. This makes horizon-flow a biased parameterization of inflation.
