My understanding of the creationist viewpoint (and they can correct me if I am wrong)is that evolution itself doesn't and didn't happen. The observed facts of evolution, whether it be the fossil record or genetic data or whatever do not fit in with a literal Biblical view that God created all the creatures that we see today, and that happened about 6,000 years ago.It's even worse if you think that there was no death before "The Fall".
It depends on which creationists you're talking to and what day of the week it is (they like to change their stories from day to day). As 6days keeps describing, in order to go from a single breeding pair of each "kind" to all its descendant species in just a few thousand years you need new species to arise
very rapidly and regularly.
Now how does that happen if evolution never, ever, ever occurs? How do you go from a single pair representing the "cat kind" to leopards, tigers, cheetahs, and
all the other species in the family? It can't be via evolution, so it must be via........? :idunno:
Then of course there's the pesky little fact that (as I noted) evolution occurs all the time right before our eyes. How do creationists deal with that? They declare it to just be "adaptation" or "microevolution". But ask them what the difference is between "adaptation" and "evolution" and you'll see so much dancing you'll think it's a party. And naturally "microevolution" is evolution, since it has the term "evolution" in it!
All of this dickering over mechanisms is irrelevant. It makes no difference how it happened. If it happened, Bible literalists and Creationists have a problem. It did happen, and they can't deal with it. So they get involved in arguments about mechanisms and statistics, since they can't deal with the observed fact of evolution.
It helps to understand that creationism is simply a type of denialism. It has no scientific merit on its own (as evidenced by its absolute lack of contributions to science in the last couple of centuries) and exists solely as a religious belief that flies in the face of observed reality. That's why when you try and get them to explain what this "creation model" even is and/or detail the evidence that supports it, they scramble around doing everything they can to turn the discussion back to evolution. When they've done that, then they can go back to the much more natural "deny, deny, deny" mode.