  We examine the circular velocity profiles of galaxies in {\Lambda}CDM
cosmological hydrodynamical simulations from the EAGLE and LOCAL GROUPS
projects and compare them with a compilation of observed rotation curves of
galaxies spanning a wide range in mass. The shape of the circular velocity
profiles of simulated galaxies varies systematically as a function of galaxy
mass, but shows remarkably little variation at fixed maximum circular velocity.
This is especially true for low-mass dark matter-dominated systems, reflecting
the expected similarity of the underlying cold dark matter haloes. This is at
odds with observed dwarf galaxies, which show a large diversity of rotation
curve shapes, even at fixed maximum rotation speed. Some dwarfs have rotation
curves that agree well with simulations, others do not. The latter are systems
where the inferred mass enclosed in the inner regions is much lower than
expected for cold dark matter haloes and include many galaxies where previous
work claims the presence of a constant density "core". The "cusp vs core" issue
is thus better characterized as an "inner mass deficit" problem than as a
density slope mismatch. For several galaxies the magnitude of this inner mass
deficit is well in excess of that reported in recent simulations where cores
result from baryon-induced fluctuations in the gravitational potential. We
conclude that one or more of the following statements must be true: (i) the
dark matter is more complex than envisaged by any current model; (ii) current
simulations fail to reproduce the effects of baryons on the inner regions of
dwarf galaxies; and/or (iii) the mass profiles of "inner mass deficit" galaxies
inferred from kinematic data are incorrect.
