The claim here is usually pretty vaguely stated. Probably the most generous is either something related to something like an appeal to looking at nature for ethics or for health
The problem is that usually, the carnist is attempting to express one of the other arguments from the A- or H- series. Without further elaboration, it's an argument of the form:
This is not a cogent argument, because neither of these premises is correct. The first premise has nothing to do with reality: putting frozen pucks of beef into a shopping cart for eating while you binge-watch the third season of New Girl covered in Cheeto dust has nothing to do with what is "natural", nor could the second premise have any grounding when plenty of things that we don't accept are "natural", such as infanticide or dying of preventable diseases.
If it's dealing with health, one can simply replace the worth "ethical" with "healthy" in the above argument, and again, largely the same counterarguments apply: you don't get nearly the exercise our endurance-runner ancestors got, you have different physiology, including the gut microbiome, and they lived to the ripe old age of "died in childbirth", since evolution doesn't favor old age, but rather reproduction.
So it's difficult to understand how this could be put forth as anything reasonable, but more information is needed to provide a more specific counterargument.