One of the strongest hints of dark matter are the CMB anisotropies and the peaks. What should a non-dark matter theory do in order to reproduce that evidence? I mean, what is the feature that a pure theory of non-dark matter should satisfy in order to reproduce the CMB results?
The main problem is that large scale structure observations tell us that non-relativistic matter makes up about 30% of the energy density of the Universe ($\Omega_m\sim 0.3$). If this was all baryonic then that would make the CMB acoustic peaks much too large relative to the low-$\ell$ Sachs-Wolfe plateau. Additionally, nuclear synthesis would be violated as the primordial abundances tell us that baryons only make up about 5% of the energy density of the Universe ($\Omega_b\sim 0.05$).