[vhcr]

Your logic is flawed, it is true that birds are dinosaurs, and it is also true that some dinosaurs are birds (literally birds). But it is not true that birds existed 200 millions years ago. The oldest known bird fossils are around 160 million years old.

[erfgh]

Why? If birds are dinosaurs then some dinosaurs are birds. So the ancestors of those dinosaurs are also birds and we can go further and further until the first living thing which was also a bird. So its descendants were also birds. So every living thing is a bird.