What Is A Bird (a k a Euornithine Ornithothoracine Pygostylian…etc.)?

My post on birds and dinosaurs yesterday led to a little debate on Facebook, including this, from paleontologist Thomas Holtz:

All living birds share a common ancestor that would also be considered a bird, so they are a monophyletic group. Nevertheless, that group is deeply nested among euornithine ornithothoracine pygostylian avialian eumaniraptoran paravian metornithine maniraptoran maniraptoriform tyrannoraptoran coelurosaurian avetheropodan tetanurine averostran neotheropod theropod...