A large part of the confusion is that dinosaurs did not emerge from birds in the same way that humans did not evolve from Chimpanzees (nor monkeys) - but rather, both groups in those pairs evolved from a common ancestor (but different ones:-).

Birds have feathers and for the most part fly, while alligators not so much. In attempting to simplify, e.g. Avians to “birds”, it causes confusion. Alligators also are not warm-blooded as birds are, not do they have beaks, all hallmarks of modern birds, but they do have four legs, long body with a tail, moveable eyelids - and don’t they have external ear openings as well? - all hallmarks of modern lizards.

Scientists use precision language like “non-Avian theropod”, but those don’t map perfectly to common words like “birds”, which everyone knows are just government drones anyway:-P.