Such genetic diversification, Snake, occurs quickly, look at the variety of pups which two mutt parents produce.
Not really, no. Labradors do not give birth to poodles.
To go back to cats, (because unlike dogs they do not [so much] suffer from human interference).
If you breed a tiger with a lion, (which happens very rarely in the wild), you end up with a liger. Now, in every instance of this event the male ends up sterile. The female is fertile.... So, you now have a fertile female liger. If you then breed a tiger with the liger you end up with a ti-liger, (only ever found from mans intervention and exceptionally rare). You could of course, (if you use a lion), end up with a li-liger. So then you end up with a sterile ti-liger. Now, if the female was fertile and you bred it with a tiger you'd end up with a ti-ti-liger, (I assume, I've never seen it done).
It really isn't as simple as you'd wish it were. What you are saying is that two cats gave birth to a lion. What then did that lion breed with? If it bred with the cats you'd end up with a mule, (and invariably the problem seen above). So what you would now have to espouse is that these two cats gave birth to two lions, (male/female), which then bred lions from then on. Then the same original cats gave birth to two tigers, two cougars, two panthers, two cheetahs etc.
If you are going to make such a claim isn't it better just to state that 2 of each animal was on the ark? After all, once we're done with cats we then have many more animals to go, (snakes etc).
Think about it for a moment.