  We show that Mannheim's conformal gravity program, whose potential has a term
proportional to $1/r$ and another term proportional to $r$, does not reduce to
Newtonian gravity at short distances, unless one assumes undesirable
singularities of the mass density of the proton. Therefore, despite the claim
that it successfully explains galaxy rotation curves, unless one assumes the
singularities, it seems to be falsified by numerous Cavendish-type experiments
performed at laboratories on Earth whose work have not found any deviations
from Newton's theory. Moreover, it can be shown that as long as the total mass
of the proton is positive, Mannheim's conformal gravity program leads to
negative linear potential, which is problematic from the point of view of
fitting galaxy rotation curves, which necessarily requires positive linear
potential.
