The paper derives the galaxy evolution by the non-interacting (incompatibility) between dark matter and baryonic matter in terms of the short-range separation between dark matter and baryonic matter, so dark matter cannot contact baryonic matter. In the conventional CDM (cold dark matter) model, dark matter and baryonic matter are interactive (compatible), so dark matter can contact baryonic matter. However, the conventional CDM model fails to account for the failure to detect dark matter by the contact (interaction) between dark matter and baryonic matter, the shortage of small galaxies, the abundance of spiral galaxies, the old age of large galaxies, and the formation of thin spiral galaxies. The non-interacting (incompatible cold dark matter) model can account for these observed phenomena. The five periods of baryonic structure development in the order of increasing non-interacting (incompatibility) are the free baryonic matter, the baryonic droplet, the galaxy, the cluster, and the supercluster periods.