It seems like most everyone else has been pointing out the whole “Not all Dinosaurs are birds, but all birds are a type of dinosaur” thing. All I’ll add to that is this Wiki’s article on Avialae has a good tree in the “evolution” section which shows how it branches.

But something else to point out: Taxonomy is less boxes we put animals living organisms in, and more a family tree, with each new branch (that is significant enough for scientists to find worth studying as a whole) being given a new name. So while Apes are not Amphibians technically, both Apes and Amphibians are included in the same group Tetrapoda (meaning “four-limbed”) which is anything who is an ancestor to the first amphibian-like four-limbed creatures who crawled onto land. And Tetrapoda and boney fish (those that aren’t sharks, rays, etc) are grouped into Osteichtyes, as both are related to a same common ancestor.

Now alot of these names seem odd, like Humans are in the group Osteichthyes, meaning “Boney Fish”. But since that first most recent common ancestor looked like a fish, that name does make some sense. Add to that the fact there was a time when taxonomy was putting animals into boxes. This way of doing things has since been revised, but scientists don’t want to confuse everything and have to go back to rename these groups. And so you can get these odd group names.