That Creationists believe in the fixity of species is an example of a common double fallacy in the origins debate. First, it is an indirect example of equivocation. Evolution, of course, cannot be proven. Throughout all of recorded history, everything has produced its own kind. Men produce men, monkeys produce monkeys, moles produce moles, so on and so forth. We have never, will never, and of course could never see the kinds of changes Evolutionists claim have happened over millions of years, mainly because it would take millions of years to see them.
So Evolutionists claim "Evolution can be seen in real time". How? Well, because organisms do produce offspring that is not identical. We see new species forming, therefore, they claim, Evolution is true. By equivocating Evolution as merely "change over time", Evolutionists imply Creationists believe in the fixity of species.
Which brings us to the second fallacy: The straw man. Let's be generous to the Evolutionist. Let's accept that literally any change over time, including the change from one generation to the next, can be considered Evolution. Well, if that's the case, not only is Evolution perfectly compatible with the Bible, the Bible actually beat Darwin to the punch by 3,200 years. Especially with regard to Esau and Jacob, the Bible makes it perfectly clear that offspring do not perfectly resemble their parents, nor even each other.
Jacob and Esau, despite being twins, were radically different from each other. In contrast to Jacob, Esau is described as red, and was hairy from the beginning (Genesis 25:25), whereas Jacob was so smooth, he had to wear fur to trick his father into thinking he was Esau. We aren't told what color he was, but as he is contrasted to Esau, it can be assumed he was not red. At any rate, despite being twins, they were identical to neither each other, nor their father.
Naturally, having stolen Esau's blessing, Jacob had to flee from Esau to avoid being killed. He took refuge with his corrupt uncle, who repeatedly changed his wages. Genesis 31:6-8 sums up the story quite well: "You know that I’ve worked hard for your father and that he has cheated me and changed my wages 10 times. But God has not let him harm me. If he said, ‘The spotted sheep will be your wages,’ then all the sheep were born spotted. If he said, ‘The streaked sheep will be your wages,’ then all the sheep were born streaked." (Emphasis mine).
Now, granted, it is God who is given credit here. But there is no evidence of any specific miracle. In fact, it wouldn't make a lot of sense of Laban to propose a deal based on what type of lamb was born if different types of lambs could not be born. It would make even less sense for Jacob to accept such a deal. So clearly, this is just a natural thing. Spotted lambs can come from unspotted mothers. Streaked lambs can come from unstreaked mothers.
A final obvious note to consider is that Genesis records the single origin of the human race. Eve, in Genesis 3:20, is called the mother of all the living. So, Moses and the Israelites, having lived in Egypt, would have known that humans change over time. Indeed, Moses' own wife was Ethiopian (Numbers 12:1).
So, for 3,200 years, the Bible has made it clear that neither humans nor animals are fixed. So, according to the equivocated definition, Jews and Christians believed in Evolution looooooong before Darwin showed up. But we don't, do we? See, as much as Evolutionists posit "change over time" as the definition of Evolution, they all know that it is actually a specific change over a specific time.
First, without the millions of years, Evolutionists have nothing. If the earth is only 6,000 years old, Evolution had no time to occur. Indeed, this is why Charles Lyell, in his mission to "free science from Moses", began claiming the earth is thousands of years old. Then Evolutionists kept increasing that age over time. So, already we see that time is an important factor in Evolution. You need far more than a generation or two for Evolution to occur.
But more importantly, it is the type of change that matters. In Evolution, a single celled organism started everything. A world with nothing but germs became a world with plants and animals, and eventually humans, all because of this magic microbe that not only created itself, but somehow managed to modify its successive generations enough to account for the diversity of life today.
Contrast that with Creation, in which you have a world that was fully populated in 6 days. Humans were already here. So were apes. So were rodents, and fish. Dinosaurs and birds lived together. Hippos and whales lived together. Creationists don't believe all life is directly related, and that descent with modification can explain anything like what we observe today. We believe God created a very good world, which began to descend into chaos after the fall.
Put another way, Evolutionists believe a world of nothing became a world of everything. Creationists believe a world of everything is gradually becoming a world of nothing. We both believe in a change over time, but Creationists believe that change is merely a reshuffling of that which already existed, not a creation of that which does not.
To prove our case, Creationists don't need to do very much. Every new species is invariably a slightly modified version of that which already exists. Blind cave fish? Ok, you had a fish with eyes, now it doesn't have eyes. Does it have legs yet? Peppered moths. Ok, you had black and white moths, they are now... black and white moths. Darwin's finches? Still finches. Wingless fruit flies? Their ancestors had wings and they do not. No matter how many times you do this experiment, you either end up with multiple versions of that which already existed, or you completely lose something that once existed, which you will never get back. You don't get Evolution from that, you get extinction. And of course, we do observe extinction.
But what do Evolutionists have to prove their case? Nothing. They don't (and can't) have Evolution happen before our eyes, and they can't point to examples of it having happened in the past.
So these "examples" of Evolution are a double fallacy. It is equivocation, because Evolution is defined in such an ambiguous manner that literally anything can be considered Evolution, and it is a straw man, because it opposes only the false doctrine of the fixity of species, which is nowhere found in the Bible, and is so rare that I've literally seen one person defend it in my entire life. Evolution is just one more act of rebellion against our Creator.
But amazingly, although He has every right to punish such rebellion, He is patient and loving and merciful. So much so that 2,000 years ago, He Himself came to Earth as a man, lived a perfect life and died on the cross. The full wrath of God was levied not upon those who deserve it, but upon Christ who did not. Through the confession of His Lordship and belief in His resurrection, we can be forgiven for all rebellion.