The chief problem with axiomatic carnist arguments is that they generally fail when applied to infants, who have properties (such as intelligence, ability to conceptualize one's own well-being, etc.) similar to animals. Carnists are quick to grant infants an exception based on "potential", e.g. "It's ok to {do X} to an animal and not to an infant because the infant has potential to eventually {do fully human intellectual thing Y}, so carnism remains ethical and "
Every able-bodied baby also has the potential to be a serial killer or nobel-prize winning writer. This is meaningless though when considering the ethical implications of something. How does the potential of what something is make something ethical or not in this context?
If potential is worth something morally, this starts to become highly problematic. For instance, is a baby from a well-to-do family more intrinsically valuable because he or she will have more opportunities? If we can identify a demographic of people who will likely end up committing a crime at some point, do we relax permissions for ethics regarding those people? This really opens up a wide array of atrocious positions that rely on circular reasoning.
Infants are a single scenario, but what about those that have mental disabilities, dementia, or people who speak a different language? Are we allowed to attack all of those people because they are unable to create a social contract with us? We then have to make exceptions for each of those, e.g. "I am allowed to eat anything that isn't:
In addition to the other exceptions you need, such as to rule out people like the Sentinelese, who are islanders that will attack anyone that approaches their island, as they are not willing to make social contracts but the genocide of whom would not be morally permissible, etc. This also doesn't take into account all of the animals that carnists would take issue with eating, such as dogs and cats, as well as the different levels of animal cruelty that some carnists would deem acceptable. It should be clear here that this is an extremely contorted and squiggly line in the sand to draw that somehow puts all humans and deliberate animal cruelty to "good" animals on one side and all "food" animals ground up into burgers on the other.
The only reasonable place to run after this is to just abandon this project of creating anything coherent out of a being's capacity and to just hold onto species or some other vague human-superior argument.