The idea is that eating animals is ok because morality is evaluated on a species-by-species basis with all members of the same species receiving the same moral benefits.
The thing that's important here is that we're ignoring emergent properties - we're not talking about how members of species X have characteristic Y, and the real criterion is characteristic Y - we're talking about the claim of species X itself being a criterion for morality. E.g. Not that we know dogs can't operate motor vehicles and therefore we restrict their ability to own a driver's license, but rather that dog-ness itself gives you some moral benefit that, say, cow-ness does not, namely the right to not be slaughtered for meat.
This claim typically arises when the carnist first presents some arbitrary criterion for deciding who can be the subject of immense cruelty (e.g. intelligence or usefulness) and when it becomes apparent that this is untenable because some humans even lack this characteristic, this species clause is invoked to close any loopholes. This is a great example.
It should be noted that this excludes conversations about conservation, but there the species is the emergent property because one is talking specifically about population dynamics. What's important in this scenario is husbandry and so the species (and genetics) itself is a criterion for selection. But this isn't what we're talking about We're talking about species being used as a proxy for morality, specifically.
If you are saying that you are allowed to harm members of a particular species in specific ways that don't extend to other species, then you maintain some burden of proof for your decision. This is particularly exacerbated by how conveniently the choice of animal and method of harm is.
We recognize so easily in any other context that such arguments are problematic because it's just asserting a position without justification. Imagine you and a friend are walking down the street when you see a shiny bright blue Porsche and your friend turns to you and says "You know, you and I have identical moral values concerning stealing cars... except I make a special exception where I morally presuppose it's okay to steal specifically cars with specifically the license plate of ABG3109... oh would you look at that?! That car right here has exactly that license plate! How convenient!" Or if it had a vanity plate then "I've decided it's okay to steal cars with vanity plates" or "I've decided it's ok to steal light blue cars on the second Tuesday of the Month... well would you look at the calendar! It's my lucky day!". It takes very little to see how poorly reasoned such an argument is.
Similarly, if you're saying that it's okay to harm animals in specific ways, then it begs for some justification.
Carnists don't actually evaluate morality by class because that's a silly thing to do in any other context. Why should the morality of individual A towards individual X be dictated by the existence or characteristics of individual Y or Z or Q that are not part of this transaction? It doesn't make sense that it might be morally impermissible to do something to an individual, but now somehow the existence of a few copies of that being with similar characteristics on the other side of the planet or the far side of the moon now changes that calculus of what is moral?
For instance, suppose we encounter some new species of a cow-like animal walking on all fours on a remote island and we evaluate them to be unintelligent enough to be locked in a cage and slaughtered for meat. But then we go to another island we find that actually, it was part of an undiscovered tribe of beings walking on two legs living in huts, making bonfires, etc. Now... is it no longer ethical to slaughter it for meat, because they are part of the same species as something more intelligent than themselves? Suppose the unintelligent copies outnumbered the unintelligent copies by a substantial number, could we now slaughter the intelligent ones for meat based on the median intelligence? Suppose then we find that these were similar animals but could not interbreed with the less intelligent species because they were too far away genetically, now are we back at ethical to slaughter the unintelligent, and unethical to slaughter the intelligent? Again, one is left to wonder: why does the existence of other members of the same species impact how one treats a being?
Or suppose a different scenario where we create a single member of a new species of animal in a lab, would it matter if we created a single one? Do sterile animals like mules have different moral characteristics because they can't give birth to a horse or any other species? Or do we make exceptions for cows and pigs since they've been grandfathered in, but we make the rule that we shouldn't add new species to the list? And if median intelligence is a criterion, how do you prove that somewhere in the galaxy there isn't a number of beings that outnumber cows on Earth that could interbreed with them but be more intelligent than humans, for instance?
Furthermore, what about how as late as 70,000 ago, there were four species of humanoids on Earth? Assuming they had the same brain capacity, if we put them in a time machine to the present, would an appropriate dividing line really be the ability to interbreed with modern humans or each other? Could we justify treating a being mentally similar to a modern human differently on the basis that it can't interbreed with modern homo sapiens?
These scenarios are all easy to answer if you seek to minimize any potential harm that may come to these beings as individuals, regardless of their intelligence, based on their capacity to suffer. But if one starts to accept that it's ok to slaughter animals for your own entertainment, then they are ignoring basic morality and painting yourself into a moral pretzel where some beings and not others can be killed without regard.
If you're free to choose species, can you also choose skin color... or ethnicity... or gender... or property ownership? What makes species a better criterion? Either it's going to be something else on the list, such as intelligence, or it'll be an arbitrary redefinition of species. One such answer is that "it's because it's what the animal can give birth to", but people of a certain skin color or ethnicity bring forth other members that look like themselves, so that doesn't answer the question, in addition to just being an arbitrary redefinition of species. And if interbreeding is a criterion, is a ring species a single "species" by this definition? And what about mules or other sterile hybrids? If we made a human hybrid in a lab, what species is it and can we eat it?
So this is already a problematic and fuzzy area, considering that we're talking about a dividing line as harsh as "you go to jail for killing a member of species X" and "you go to jail for stopping someone from killing a member of species Y" (or "let's put species Y in a jail purely for the entertainment of species X").
Ask a carnist if they'd eat a golden retriever and most would say no. But coyote hunting is a thing, and most carnists won't object to it, even though coyotes, wolves, and dogs are all the same species. And there are plenty of cases where carnists don't grant different members of the human species the same rights, such as infants, people of different genders, or people with developmental disabilities. So the carnist is then making additional moral decisions based on emergent properties specific to those members of the species.
So, if you're keeping track of this pretzel: we now have another layer of emergent properties for moral decisions, in addition to the "species" property. And this "species" property comes from averaging together the members that you can arbitrarily interbreed with. It would then seem as though "species" is just conveniently used to close the loophole that is created when one okays unnecessary animal cruelty.
Again, if one seeks to minimize harm and maximize well-being by treating these individuals with respect, then that makes that entire question significantly easier.
This argument still doesn't take into account the ecological and human impact of eating meat, and it remains unethical for those reasons as well.