Why doesn't the coronavirus affect animals like dogs and cows? I know that the SARS-CoV-2 is a zoonotic virus i.e. it can affect both humans and other animals. I also know that the DNA composition and cell structure of almost every animal on earth is the same.
Even though the DNA sequence may be 90+% similar between two species, individual amino acids can make a huge difference in the interaction between two proteins. In this case, the most relevant proteins are the coronavirus spike protein and the ACE2 enzyme expressed on the surface of target cells. Even in the limited amount of time SARS-CoV-2 has existed and been studied, researchers have found single amino acid mutations in its spike protein that meaningfully affect how well it binds to ACE2. When constructing animal models for COVID-19, and for the original SARS, in some cases it has been necessary to introduce a human ACE2 gene to allow infection. It is worth noting, however, that this is not always the case--for instance ferrets and hamsters can be infected by SARS-CoV-2 without any genetic modification at all.
This paper gives a summary of the work so far: Muñoz-Fontela, C., Dowling, W.E., Funnell, S.G.P. et al. Animal models for COVID-19. Nature 586, 509–515 (2020).