An argument that you may or may not have heard before is that "disproving evolution proves creationism." Kent Hovind, for example, made this argument in his debate against Michael Shermer when he said the following:
"Design in nature is impossible to explain without a designer, and the idea of creation is true because of the impossibility of the contrary. It is impossible that there not be a creator for something like this."
And this mentality is clearly taken for granted when you see how many religious people argue for their position. Very rarely do you see religious people presenting actual positive evidence in favor of creationism. More often, they instead try to refute evolution by saying things like "There's no evidence that macroevolution has taken place", "Beneficial mutations are too rare to occur by chance", "There are no transitional fossils", and so forth—none of which are true, by the way.
This argument is problematic primarily because it sets up a false dichotomy between godless evolution and divine creation. This dichotomy is flawed in many ways. First of all, evolution isn't necessarily godless; one could imagine a god guiding the process of evolution—which is something that many religious people do believe, because they're well aware that the evidence that evolution has taken place is incontrovertible. And creation isn't necessarily divine, either, as perhaps advanced extraterrestrials could create life-forms. You could also have creation AND evolution if, for example, the original life-forms were created, while all subsequent life-forms came about via evolution.
But more importantly, creation and evolution aren't the only two possibilities; thus, this isn't a true dichotomy. There could be other potential explanations for how the diversity of life on our planet came about. One example is the idea of spontaneous generation, which had many believers up until the 19th century or so. The basic idea was that flies originated from rotting meat, mice came about from bales of hay, mosquitoes were spontaneously generated by swamps, and so forth. While we might laugh at this idea today, it's actually quite intuitive, as the hypothesis built a bridge between the observation that certain organisms were often seen in close proximity to certain environments. Thus, it was thought, perhaps these environments somehow cause these animals to spontaneously originate? Perhaps the rotting process of the meat in combination with heat from the sun causes its atoms to be rearranged and form the body of a fly?
This hypothesis was eventually refuted in part by some very simple and clever experiments performed by Louis Pasteur in 1859, in which he put a sterilized nutrient broth in two containers, one of which was exposed to the outside air, with the other being sealed off. He found that the exposed one became clouded with microbes, while the sealed one did not. So this hypothesis has since fallen into disrepute, but it nonetheless is an example of another potential explanation for how the diversity of life on our planet arose.
But even if we were in a situation where it appeared that there were only two competing explanations, it still wouldn't be justified to treat this as a true dichotomy, because it could simply be that the true explanation is one that we haven't yet thought of.
Evolution or creationism is not a true dichotomy; evolution or not evolution is a dichotomy. The way we can tell that this is a true dichotomy is that there are no third alternatives; the explanation is either evolution or not evolution. Think about it as analogous to a standard light switch: The light switch is either on or off. There's no third option. There's no third or fourth direction that we can move the light switch in. There is no state that a light switch could be in that's not either on or off; it's necessarily one or the other. And it also can't be both at the same time. And if the light switch is on, we can also say, with certainty, that it's not off; if it's off, we can also say that it's not on.
But the thing about the explanation "not evolution" is that it isn't specific. It doesn't tell us what the explanation is; it only tells us what the explanation is not. And this space could potentially be filled with many different explanations, as the example of spontaneous generation illustrates.
An obvious point that follows from this is that disproving evolution wouldn't prove creationism. Thus, in order to substantiate creationism, the creationist needs to actually present positive evidence in favor of their claims. Let's just imagine that we wake up tomorrow and we read in the newspaper that every scientific publication on evolution for the past 150 years has been a complete hoax. Every fossil was a fabrication, all the data from every experiment was faked, we were totally mistaken about every act of evolution that we saw before our very eyes—let's just imagine that all of the evidence gets completely falsified. This is, of course, inconceivable as anybody who has actually studied evolution knows, but let's just imagine it. By disproving evolution, creationism wouldn't automatically become substantiated. We wouldn't say "Well, now that evolution is false, we know that creationism must be true", and this is because, to reiterate, these positions aren't dichotomous.
Imagine, by analogy, that a crime was committed. Police have two suspects in custody: Suspect A, and Suspect B. After interrogating them, they find out that Suspect A's alibi checks out: he was on vacation in Costa Rica at the time that the crime was committed, so he couldn't possibly be responsible. This doesn't automatically mean that Suspect B is guilty. They wouldn't say "Well, if Suspect A didn't do it, Suspect B did. Off to prison you go!" Exonerating one suspect doesn't incriminate another, because maybe instead of Suspect B, Suspect C is actually guilty, or Suspect D, etc. And this could be the case whether or not the guilty person is even in custody or under suspicion, just as the explanation for the diversity of life could, in principle, be something that we haven't yet thought of yet. In order to demonstrate that Suspect B is guilty, you need to actually present evidence that he committed the crime: blood samples from the scene of the crime, surveillance camera footage, etc.
Similarly, for evolution vs creationism, in order to demonstrate that a claim is true, you have to actually provide supporting evidence in favor of your claim. Perhaps, for example, a cryptologist could point out that all organisms share a sequence of DNA that somehow translates into "This organism was created by the God of the Bible." Or perhaps a creationist could present undoctored video evidence of God appearing before them and creating an organism.
But creationists very rarely attempt to substantiate creationism. The only example that I can recall ever hearing of any creationist attempting to present positive evidence in support of creationism is an appeal to scripture. Aside from that, I genuinely can't think of any other examples. If you can, let us know in the comments section. But before you start rattling off the traditional arguments, please understand that trying to poke holes in evolution or arguing that evolution doesn't sufficiently explain a phenomenon is not the presentation of positive evidence in favor of creationism. This is a very important distinction to understand.
What creationists don't do is collect observations and perform experiments whose results reject a null hypothesis and lend support for their hypothesis. This is no coincidence: Creationists don't support their claim through scientific research because creationism is fundamentally unscientific. And forget scientific research; even if we set the bar much lower than this and ask for any examples of evidence being provided in support of creationism, aside from an appeal to scripture, the response is *chirping crickets.*
So to recap, disproving evolution wouldn't prove creationism because the two ideas aren't truly dichotomous; there could be other explanations for the diversity of life on earth than these two. In order to substantiate creationism, creationists need to actually present positive evidence in support of their claims—which they rarely even try to do.