The word 'creationism' has become a bait-and-switch term in the mouths of certain people. It first gets used to mean some very general thing when you figure out who counts (i.e. someone who believes God created or someone who believes God fashioned the universe via some means that wouldn't be likely if naturalism would be true). But then it gets applied as if it means a much more specific view, one seen as implausible by many who hold to creationism in the broader sense. When you want to say bad things about all the people who count in the more general sense, you call them creationists, and thus you associate them with those who hold to the more specific view that's much less tolerated.
For the sake of this post, I'm reclaiming its meaning in the general sense as perfectly legitimate for all who believe God created the universe. It therefore applies as much to those who accept a divine explanation behind the standard scientific account of the natural causes of human origins as much as it does to those who accept a supernatural method to begin with.
Now here are some possible views:
Naturalism: God doesn't exist, and so God had no role in human origins.
Non-creationist theism: God exists, but God didn't guide the origins of human life in any significant way, certainly not with any intention that we or any beings like us would come along.
Barely-creationist theism: God did guide along the causal processes that led to human life to some degree, but God had no concern for that aspect of the process. We're just a side-effect.
Creationist evolution: God fully guided the process of human origins by means of the standard scientific model (or something close enough to it), including natural selection and common descent of humans from animals, with the goal of producing the life forms that resulted, including human beings. Random chance, as usually thought of in evolutionary theory, is really just statistical frequency, with God guiding the process. This view is sometimes called theistic evolution, but that name technically applies to the above two views as well.
Old-Earth, non-evolutionary creationism: The Earth is as old as the standard scientific account takes it to be, and the universe is as old as the standard scientific account takes it to be. But the standard scientific account is wrong about human origins. The mechanism usually described as natural selection and random chance (which is really divine guidance) are real and observable on the small scale, but inter-species evolution did not occur (or, on a variation, it occurred for other animals but not for humans). This view is sometimes just called Old-Earth creationism, but that view technically could apply to the above view (or even the above two).
Young-Earth creationism: The Earth is about 6000 years old, and the creation framework of Genesis 1:1-2:3 describes God's creation process chronologically and with the creation days of the poetic narrative corresponding exactly to 24-hour periods in real time. Sometimes this view is simply called creationism, but that name could apply to all the views in this list except the first one.
Those who hold to the young-Earth model criticize all of the other above views. Here I'm interested only in biblical arguments. Naturalism is easily ruled out biblically, since it denies the very existence of God, and non-creationist theism and barely-creationist theism also seem a little hard to fit with the biblical view of God creating human beings with particular intent. So among those who accept the Bible as authoritative, you're not going to find very many people who accept any of those views, even if conceptual space allows for them.
I'm interested in the arguments Young-Earth creationists use to argue against the other two remaining views. They argue that those two views cannot be held consistent with a high enough view of the Bible as authoritative and infallible scripture, and I can think of three arguments along those lines.
One argument targets common descent, because they think "created according to their kinds" cannot mean that animals were created according to their kinds by means of creating other species first and then slowly evolving them to new kinds. The above sentence would be meaningless if it couldn't mean that, and it's not, so I think that debate is easy to resolve. It can indeed mean that.
The second argument is directed against all old-Earth views, namely the less-than-convincing argument that Genesis 1:1-2:3 has to be taken so that the days within that account must refer to periods of time rather than an organization according to theological purposes. You first have to assume that it means 24-hour periods within the text's framework, which I think is indeed plausible, indeed almost certain, but then you also have to go beyond that to assume that the text's framework corresponds to an actual chronology rather than a theological organization according to the themes the author intended to bring out in contrast with similar creation myths from the time. It's the second assumption that I don't see a strong enough warrant for to counteract the overwhelming scientific evidence for a contrary view.
But there's another biblical argument against old-Earth views that I think has more punch to it. Old-Earth views require animals to have been around for much longer than human existence, killing and eating each other. I suppose there's no absolute requirement for that. Maybe they just had the teeth for carnivorous lifestyles long before they needed them or something, because God foresaw what they would need for after the fall. But such a view seems unlikely to be true. So it seems the fossil record as it stands does require believing that animals killed and ate each other before the first human sin, and animals would have been as much as a threat to the first humans, it seems, whether humans were created wholesale out of dust or out of dust by means of a long chain of natural selection and random chance moving through different species until you got the level of complexity of a human being.
The problem is that the biblical narrative does seem to assume that death came as a result of the fall. So it seems there's a conflict between the biblical narrative and the old-Earth view, even the old-Earth view denying common descent. This isn't just from Genesis 3 saying that death is a result of the fall. Isaiah 11 has the wolf, lamb, and leapard lying down with a young goat in the restored creation undoing the fall, and children play with snakes, with lions eating straw. It's as if the fall is undone, and part of that is undoing carnivorous animals' diets.
There are a number of things old-Earth views have had to say about this problem. One that I think makes some sense is that the Garden of Eden might have been a special place protecting humans from this, where the animals present were different miraculously. It's only human death that the fall brought on, not all death. But that doesn't solve the problem of how restoration undoes carnivorism, when carnivorism was never part of the fall.
It occurred to me when reading Isaiah 11 recently that this assumes something that most Christians don't actually believe. Hardly anyone who holds the Bible in high regard takes the human fall to be the first fall. How did the snake get to be tempting Eve to begin with if there was no sin in the world (and thus no death in the world)? We have to infer an angelic fall from elsewhere in scripture (although I don't think Isaiah 13-14 is a legitimate place to find direct support for that). I wonder if the use of the snake image for the tempter indicates that this angelic fall did affect non-human animals, and God generated human beings (whether by direct creation out of dust or by means of descent from animals affected by the fall) in such a way that human beings were not fallen (after all, animals here aren't fallen, just affected by the angelic fall).
Putting that together with some special provision in the Garden for removing the affects of the angelic fall from animals, I think the problem is pretty much resolved. I'd grant that it's a bit complex to be the most natural thing you'd think from reading the text. However, the issue here is never just the most natural reading of the text vs. a less-plausible reading of the text. It's a whole set of issues that complicate each other. You have the most natural reading of the text on one side with a completely impossible reading of the scientific evidence, and then you have a less-natural but certainly-possible reading of the text with a rather straightforward reading of the scientific evidence on the other side. Unless you want to make our interpretation of the Bible infallible rather than just restricting that infallibility to the Bible itself, it seems the less-plausible but possible reading of scripture with the possible interpretation of the scientific evidence is much more likely than the more-natural reading of scripture with its impossible reading of the scientific evidence.
So, although I said this objection has more force, I think there's enough to say about it that I don't think it's decisive or even worth all that much time worrying about. Those who hold to a high view of scripture can without too much effort accept either of the old-Earth views without this objection really being a problem.