So, dogs produce dogs? Okay!
Our household pets are
FAMILY: Canidae (Dogs, Wolves, Coyotes and Foxes)
GENUS: CANIS (Dogs, wolves and Coyotes, but no Foxes).
SPECIES: Canis Familiaris.
So, "each after their own kind" and dogs give birth to dogs, so therefore, "Kind" must mean "Family".
Let's apply this to humans, okay?
SPECIES: Sapiens; Got it!
GENUS: Homo (Hey! We're All Homos! JK; okay, includes Modern and Archaic humans ... Uh, well, wait ... Evolution deniers don't like that, even though it's fine for dogs ... Interesting ...)
FAMILY: Hominodea (Great! Hominodea includes Humans and Apes and Gibbons!)
So therefore, "Each after his own kind" includes Humans, Chimpanzees, Orangutans, Gorillas and Bonobos!
But wait, no, because these are not of the same "kind" even though they fall under the same taxonomic scale as "Dogs" where we defined "Kind" as "Family" but suddenly it doesn't work for Humans ...
This is how worthless "Kinds" is in discussing this issue. "Kinds", in the context of Evolution discussions, can mean anything we want it to mean. It creates a nonargument where the one side can move the goalpost wherever they want to move the goalpost and the other side is left trying to get the goalpost to sit still a minute while chasing a greased pig. This is how worthless "dogs came from nondogs" arguments are, as in this context, the definitions of the words within the argument are nonspecific.