Cladistics is simply one approach to biological classification. Another is phylogenetic (or phenetic if you wish) taxonomy. That phylogenetic taxonomy happens to be older than cladistics doesn't mean it lacks validity, and it's a grave mistake to refer to cladistics as "
the classification system." Whether one uses cladistics or phylogenetic taxonomy depends on what one wants to say about the relationship among organisms.
Only because it's specifically aimed at reconstructing evolutionary histories, to which I can only say, of course it is, but so what?.
Nope. The most that can be said is that they are both members of the same clade. Thing is, there comes a point in the evolutionary process where an organism no longer possess those characteristics that define its ancestor, and, in fact, has developed characteristics inapplicable to its ancestor. And it's these differences that give us reason to use different words---"bird" and "dinosaur" in this case--- to distinguish them. We call animal
A a bird because it has those defining characteristics of birds. and we call animal
B a dinosaur because it has those defining characteristics of dinosaurs.
Thing with clades is that, time wise, one can construct them as large as one wants. One could construct the clade that includes birds to not only include dinosaurs, but
their progenitors, the archosaurs, animals not considered to be dinosaurs.
The archosaur Postosuchus
And going back even further in time one finds that the archosaurs evolved from the diapsids about 237 million years ago
The one foot-long diapsid Petrolacosaurus
So, how about we call birds diapsid reptiles because they belong to a clade we could construct that includes both?
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