This enthymeme particularly bugs me, and most often comes up with Creationists: Many seem to think that a species can't change, like there's some barrier that trims out any mutations beyond some arbitrary limit to diversity. The problem is that "species" is a loose label humans invented for convenience.
Let's take horses, for example. If you were to introduce a person without preconceptions to a horse and a zebra, it probably wouldn't be surprising if he thought they were the same species, just with different fur patterns. They are in the same genus, so they do have a lot of similarity. But they are different species, since they can't produce fertile offspring. Take dogs as well: Thanks to human breeding efforts, they come in a vast variety of forms, but many can interbreed. Naturally, with that variety, it's not hard to convince some people that some breeds aren't dogs at all.
Given what humans have been able to do with canines, just how flexible is this "species barrier?" And where's the magical stop sign that prevents anything from going outside it? Or is there some magically unalterable "species" DNA that isn't subject to nonlethal mutations? The problem isn't finding these things: It's that many Creationists don't understand that our labels are based on convenience, not on immutable laws or some quintessence a particular group of critters are supposed to have. Life is a moving target, and is not tethered down by squiggles on a page or patterns of sound issuing from a human's mouth. Truename Magic does not exist.
There are a bunch of living things out there. We just lump them into categories to make it easier to talk about. Mr. Ed is a horse. Fido is a dog. We know Ed's DNA is compatible with these other things we call "horses" because they contain the same characteristics we use to define him as a "horse." Just because we invented a word to describe this compatibility doesn't mean the horses are now obligated to conform in every way. With enough time, some horses might lose some of those characteristics (but not all, since, say, becoming a protostome instead of a deuterostome would kill the offspring) and become incompatible, necessitating a new species or genus name.
The objects we describe are real. The words we use to describe them are a convenience. If something defies description, it's the description that's the problem.