A major stumbling block for Evolutionists is that they rarely understand the beliefs we have in common. To many Evolutionists, any change at all, even the fact that you look slightly different to your parents, is adequate proof of Evolution. Cave fish have no eyes? Evolution. Finches have thick beaks? Evolution. Moths can come in different shades of black and white? Evolution. These common examples are all supposedly proof of "Evolution", but the truth is, this is not Evolution. At least, it is not the kind of Evolution that is opposed to Creationism.
Let's be generous to the Evolutionist for a moment and say that different species of finches are Evolution. This is a change at the species level. But as shown in the above diagram, species is the lowest level of the Linnaean taxonomic system.
Contrary to popular belief, Creationism does not require the fixity of species. In Genesis, God created living organisms with the intention that they reproduce according to their kinds. This is where Evolutionists tend to get angry. According to them, the term "kind" is just something Creationists made up (which makes this an excellent time to point out that Carl Linnaeus, the father of taxonomy, was a Creationist, which means that the taxonomic classification system Evolutionists still use today is also a system a Creationist made up).
While Evolutionists attempt to make it sound like Creationists are just trying to make up some ad hoc response to Evolution, "kind" is not a new term. It is the English translation for the Hebrew word "min", as has been written in Genesis for more than 3,400 years now. In other words, it's actually older than the modern Creation/Evolution debate.
But what is a kind, and how does it relate to the Linnaean scale? Unfortunately, this is not an easy subject. Linnaeus defined species as "a stable, reproducing population, not interbreeding with other populations." This is because every time the word "kind" is used in the Bible, it is directly related to reproduction. Organisms were said to reproduce "according to their kinds", and when Noah was collecting animals for the ark, God commanded him to take two of every kind to be kept alive with him and his family, preserving them through the flood.
Thus, Linnaeus wasn't too far off. But here's where it gets tricky. If an organism is able to reproduce with another organism, they are the same kind. However, losing the ability to reproduce does not mean two species are not the same kind. So what is a kind exactly? A number of proposals have been put forward, and Creationists have ultimately founded a field of research called "baraminology" to determine exactly which animals belong to the same kind. Eric Hovind uses the definition "the organisms that were originally able to reproduce when God created them." My own definition is similar: "A grouping of organisms that carry the relevant genetic information to continue filling the earth."
But isn't this circular? A kind is animals that are related by reproduction, but reproduction determines which are the same kind? Yes, it is circular, but this doesn't make it unreasonable. Natural selection is also circular: The animals that are fittest survive, and the animals that survive are the fittest. This is circular, but is also observable.
In the same way, it is observable that creatures reproduce according to their kinds. Cats produce cats. Dogs cannot reproduce with cats, but can reproduce with other dogs, resulting in the production of more dogs, not a litter of platypuses. Donkeys can reproduce with zebras, which makes them the same kind, but no zebra has been, or ever could be successfully bred with a crocodile, which will never have the genetic capabilities to evolve the anatomy required for flight, as much as a genetic mutation may eventually erase the genetic information for said crocodiles to grow legs, which could, theoretically, be selected for under the right conditions. Thus, although circular, it is not outside of reason because it is in line with science. We can observe creatures reproducing according to their kinds, just as we can observe survival of the fittest.
So, what kind of change would falsify Creationism and demonstrate Evolution? Because of the imperfections of both the Linnaean scale and the relative newness of the field of baraminology, neither of them really line up. But we can simplify this in a way that reasonable Evolutionists can level with. Both Creationists and Evolutionists share the Linnaean system. It's not like we pretend the Linnaean system doesn't exist. Why should we? One of our own literally invented it, so it would be more appropriate to try to take it back from the Evolutionist than to reject it. On the Linnaean scale, we don't deny that species change. Among Creationists, there is generally agreement that kind is around the family level, though in some cases it does reach the order level.
But Evolutionists don't just believe two similar species may share a common ancestor, as Creationists do (and did before Darwin). Evolutionists ultimately believe all life is descended from one common ancestor; a single celled organism that was created by some unknown natural mechanism about 3.8 billion years ago. In other words, the difference between Creationists and Evolutionists is our "trees of life".
With Creationists, there is an "orchard". All humans can trace their origin back to one original pair; Adam and Eve. But they were created directly by God. Thus, they are the trunk of our family tree. Planted next to our tree might be the dog kind. Planted next to that, the cat kind. Frogs, mice, giraffes, each of these are all grouped into their own, independent kinds, which may show some variety, but are not all linked together.
With Evolutionists, however, there is only one tree. All living organisms are one big "happy" family. You're related to your brother, your cousin, your friend, your enemy, your dog, your cat, your goldfish, and that banana you ate for lunch. And they call this science...
But perhaps the reason Evolutionists scoff at the concept of baraminology is because they know that universal common descent is not science. See, showing that one species is related to another species is not the same as showing one family is related to another family. The kind of change Creationists believe in allows for horses to be related to donkeys, it does not allow for dinosaurs to be related to birds. Basically, the higher up the Linnaean scale you go, the harder it is to prove relationship between each group. But Evolutionists want to take it all the way to the top! They don't just believe that Jews are related to gentiles with Adam and Eve being our common ancestor, like Creationists do. They don't even just believe humans are related to chimps, as Darwin did. Evolutionists believe that all life is descended from a single, self-created common ancestor, which means while we all believe "Evolution" occurs at the species level, the onus is on Evolutionists to prove that it occurs at the domain level.
But this has never been observed. It has never been observed because it simply cannot occur. And Evolutionists know it cannot occur. So they attack the field of baraminology because that way, they can continue to argue that any change can be considered "proof" of Evolution. "Of course Evolution happens, it happens right before our eyes!" But no. No it doesn't. All we observe is change within kinds, a concept that is perfectly in line with the Bible.
But taxonomy isn't really the focus of the Bible. Rather, the Bible is supposed to explain our relationship with our Creator. When God created man, man sinned, severing our relationship with Him. Each and every one of us, just like Adam and Eve, sinned against Him, meriting death, both physical and spiritual. But the glorious thing about God is that He loves us all the same, and so He doesn't want to dispose of us. 2,000 years ago, the Son of God was born on the earth as an innocent baby boy. He maintained that innocence, sinning a grand total of zero times during His life. But He died anyway. He died a brutal death by being nailed to a cross, a sinner's death for a man without sin. Then He rose again. Through faith in the death, resurrection and Lordship of Jesus Christ, we can be completely forgiven for our sins and inherit eternal life in the Kingdom of Heaven. Now, does that really sound like something worth throwing away because some finches have bigger beaks than other finches?