(Abridged) The existence of exotic dark matter particles outside the standard model of particle physics constitutes a central hypothesis of the current standard model of cosmology (SMoC). Using a wide range of observational data I outline why this hypothesis cannot be correct for the real Universe. Assuming the SMoC to hold, (i) the two types of dwarf galaxies, the primordial dwarfs with dark matter and the tidal dwarf galaxies without dark matter, ought to present clear observational differences. But there is no observational evidence for two separate families of dwarfs, neither in terms of their location relative to the baryonic Tully-Fisher relation nor in terms of their radius--mass relation. And, the arrangements in rotating disk-of-satellites, in particular around the Milky Way and Andromeda, has been found to be only consistent with most if not all dwarf satellite galaxies being tidal dwarf galaxies. The highly symmetric structure of the entire Local Group too is inconsistent with its galaxies stemming from a stochastic merger-driven hierarchical buildup over cosmic time. (ii) Dynamical friction on the expansive and massive dark matter halos is not evident in the data. Taking the various lines of evidence together, the hypothesis that dynamically relevant exotic dark matter exists needs to be firmly rejected.