Please prove here why cats will never give birth to dogs, even given millions of years and evolution, using your knowledge of genetics, evolution, statistics, mutations, phylogeny...
For the same reason that spanish speaking parents will not be raising a chinese speaking child.
For the same reason that when you give birth to a child, that child will not be your cousin.
Now consider this:
Spanish and italian both derive from Latin. Yet both are distinct languages. The distant ancestors of extant spanjards and italians, spoke latin. During a time that neither spanish nore italian existed.
Now get this:
at no point in history, did a latin speaking mother raise a spanish speak child. at no point in history, did a latin speaking mother raise an italian speaking child. In fact, EVERY child that was brought up, was brought up speaking the language of the parents that raised said child.
And yet today, they speak spanish, italian, french, portugese.... but not latin.
So how did that happen, knowing that EVERY child that was ever brought up, ended up speaking the language of the parents that raised it?
How did Latin transform into these 4 distinct languages, if no latin speaking parents ever raised a spanish speaking child?
When you can answer that question, you'll understand how cats will never give birth to non-cats. Or in more generic terms: you'll understand why members of species X will be producing more mombers of species X.