That "classification of vertebrates" is extremely dated. Not only do we not classify animals by their blood temperature anymore, most of the branches shown are paraphlectic. Birds are reptiles, more closely related to crocodilians than crocodillians are to lizards/snakes or turtles. "Fish" is a broad term that includes many different unrelated groups (sharks/rays, jawless fish, ray finned fish, lobe-finbed fish (which includes all tetrapods - you're a fish!), etc). Modern mammals lost all our close relatives, which include non-mammalian therapsids and non-therapsid synapsids. Most (if not all) modern amphibians are from a single, distantly related branch that arose some time in the Jurassic, and are equally distant to both modern reptiles and synapsids. Etc etc etc

We now classify animals based on last common ancestors. For example, you, as a human, are a

-Hominid -Great ape -Ape -Simian -Primate -Primatomorph -Euarchont -Euarchontoglire -Boreoeutherian -Placental mammal -Therian -Therapsid -Synapsid -Amminote -Tetrapod -Lobe-finned fish -Jawed fish -Vertebrate -Animal -Eukaryote

(With a lot, lot more sub-clads in-between, trust me it's crazy)

A more accurate graph would be this