No. And no one ever said otherwise.
The Theory of Common Descent says that cats and dogs are both descended from a common ancestor. But the ancestor didn't look like either of them. Dogs don't contain the genetic information that defines a modern cat. It would take a stupendously unlikely set of mutations to recreate that exact genetic information.
(There are cases of convergent evolution. For example, there was a sabertooth marsupial which looked a lot like a "sabertooth tiger" did. But the details were different, and it was still a marsupial.)