The idea is that carnism is some sort of default position and that hurting animals doesn't require justification. Au contraire vegans need to justify veganism.
The vegan argument is a position of not buying the idea that you can't harm specific animals in specific ways without justification. The problem with arguing against this is you probably already agree with it for the vast majority of animals and definitely for humans, and the vast majority of ways you could harm one's well-being. (This argument still works for other reasons if you pretend you don't) Wherever you draw the line, you need to then justify this very contorted lasso you draw around those specific animals and those specific purposes. Without said justification, this is all just special pleading.
It should be noted that one maintains the burden of proof in cases when they are blatantly special pleading. If you start picking and choosing this buffet-line ethics of "ok to harm this specific animal, not okay to harm this other one", "ok to kill and pose with a selfie with this particular set of animals but not these others", or "can kill this animal but can't beat this animal" then it's incumbent upon you to show why this is the case and what specifically you are basing your criteria on.
For instance, how would this position deal with throwing baby chicks alive into shredders (a common egg industry practice)? It's hard to imagine that this statement has some default position of "not immoral" and that one would somehow have to "prove" that shredding animals alive is bad. In the year 2500 when people are zipping around in flying saucers eating 3D printed food or whatever, do you think that we'll look back and go "you know, I think the people arguing that eating animals was wrong were losing their minds. The obvious, clear default is to put a bolt though an animal's head repeatedly until it stops moving so you can slice its throat open, all as a means to turn 10 calories of plant protein into 1 calorie of meat.
Again, we can look back at even animal atrocities like dog fighting in medieval Europe, poaching that was prevalent in colonial countries thereafter, clubbing seals for food, or (even in our lifetimes) capturing and imprisoning orca whales in a swimming pool smaller than the visitors' parking lot. We look back on these and think "yeah that probably wasn't exactly the most ethical thing to be doing". We would agree that these positions were probably not the default. Is eating animals any different? Are you really sure it's not going to make it onto such a list?
Present any set of moral axioms. Examples include:
They all immediately speak to veganism by default. That is, until one rolls up their sleeves, gets in there, and starts tinkering to qualify out animals: "well, when I said that we try to minimize suffering and maximize well-being... I really just mean humans... but if intelligent aliens came around I would include them too, So I mean I guess intelligence is the criterion, but only sometimes because we can't eat unintelligent humans..." and the pretzeling up commences, listing off a litany of rationalizations for why animal cruelty for one's own entertainment is justified.
Not hurting animals is the default and simplest argument under literally any reasonable moral system, and the desperate search for justification is the mountain that carnists try to climb every time they invoke morality.
And therefore all the same problems apply.