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Why do you think that all the birds came from a common ancestor?
A model of a nesting oviraptorid dinosaur.
This feathered model from a Museum exhibition shows how an oviraptorid dinosaur may have looked when it was alive.

Think of it this way. Or draw it. If every animal that has feathers has a backbone but all animals with a backbone don't have feathers - what we're are saying is that both feathered and non-feathered animals come from a common ancestor with a backbone. The simplest explanation is usually the right one. Why? Think about it. Is it likely that feathers evolved 15,000 different times in each kind of bird species? Feathers evolved once, and all feathered creatures descended from that first feathered animal, changing other characteristics in response to its environment.