Why do they say that the tyrannosaurus rex is a long ancient ancestor of modern day chickens?

The common ancestor thing is hard to wrap my brain around. Dawkins gives a cool thought experiment where he says imagine a card catalog with photos of you and your ancestors in chronological order. If you look back 10 generations, you'll find a human. If you go back 100 generations, you'll find a human. If you go back 5,000 generations, you'll still see a human! However, they probably won't look exactly like a moden human. If you go back 15,000 generations, you'll find something human-like, but not really a modern homo sapiens. All of those cards along the way have miniscule,imperceptible differences. If you go back far enough, you'll find something like a rodent. But the number of cards you need to flip through to find that rodent is extremely large. Something like 200 million generations. Keep in mind the more ancient animals had shorter life spans.

So t-rex and chickens may have come from the same branch, but there are millions of "cards" between them.