Clades are used for classifying birds and everything else, it’s just a little messier than the neat Kingdom/Phylum/Order/etc way of laying out evolutionary history. If you think of a species as being a specific pinpoint on the tree of life, clades are more like drawing a circle around a lot of pinpoints and branches.

But yeah, biology is nothing but ‘the last thing we taught you was an oversimplification!’ all the way down.

We do, a clade is just a group consisting of an ancestor and all its descendants. So basically, the evidence indicates that birds are all the descendants of a more traditional dinosaur and are more closely related to more classic dinosaurs like t Rex and velociraptors than those dinos are to ones like brontosaurus.

In part this is done by examining physical characteristics in fossil specimens and seeing where traits seem to appear and how they seem to evolve over time. Like it’s obvious that marsupials are more closely related to us placental mammals than either are to birds or reptiles. After all we give live birth and have hair and milk. And both groups are more closely related to each other than egg laying mammals (monotremes) like platypuses, but that all three are more related to each other than birds, alligators, and lizards. And you can keep going looking at less and less obvious traits. And eventually you see that a weird division in how jaws work happened in the Paleolithic that separated these two clades, and that actually dimetrodon is more closely related to us than to dinosaurs.

And since you can do stuff like that you can see that in the jurassic a group of theropod dinosaurs started evolving feathers, and some even evolved beaks and wings. And by the cretaceous some of these dinosaurs were what we’d call birds today. And even better for them, many were small generalists, which we suspect is the best thing to have been at the end of the cretaceous as species fitting that description seemed to survive the best during the extinction event.