"Name the trait" is the name of a common vegan argument in which vegans ask carnists to name the trait that gives humans special rights. The claim here is that it's impossible to fulfill this request without some fundamental understanding of consciousness we don't already have
It doesn't actually matter whether or not you can answer this question (for most carnists) because they implicitly accept that some animals have some moral rights to not be deliberately tortured or factory farmed, therefore they would reject out of hand this argument for cutting the fins off a dolphin to watch it suffer, for instance. So this argument would only apply if you were trying specifically to claim that all animals have no moral rights whatsoever. As soon as you take a position that grants some animals some moral rights, you immediately lose the ability to make this argument, because you've admitted that given their level of consciousness, we have some moral obligations towards them.
Also, it doesn't matter because if we just allow for a human with an intellectual ability to have (more or less) identical consciousness to an animal, we would not say that we could then hang them upside down and slit their throat. So you would need to implicitly accept that as ethical as well if you were to remain consistent.
So, if you believe either of those things (that some animals have some rights or that humans with equivalent consciousness to animals have special rights), then you would need to instead make an argument that rules out certain animals over others and certain actions over others.
The point of "name the trait" is that the carnist makes an unsubstantiated assertion when they special plead the rights of some groups over others. So to then say "Well I don't have enough information to justify my assertion" is a bad argument when you're the one with the burden of proof.
It also is pretty obvious that this maintains the burden of proof because you could always assert that we just "don't know enough about consciousness", and you could just always assert this no matter how much we learn. We already know a great deal more than we did a century ago regarding the neurophysiology of people and how different areas of the brain interact when people are or aren't conscious. But that's not enough, right? You can just always move the goalposts. So to then say that this burden of proof is unsolvable is to essentially make the vegan's case for them. Typically, if you disagree with someone, making their case for them is inadvisable.
We recognize this is a bad argument in any other context. "Is stealing a car immoral? We would need to know some fundamental truths. What actually is a car and where does "car" end and "SUV" begin? Is an "SUV" a car, and if it is is a "truck" a car as well? We'll never know. What does "Is immoral" actually mean? Also, What were they planning on doing with the car? We can never know if they were going to do something worse!" This is just putting as many feeble defenses up as possible. In most other contexts, these kinds of defenses where someone keeps asking off-the-wall questions that we can "never really know" would make for funny sketch comedy, not a serious argument. It's a little less funny when someone is paying for animals to be stuffed into a shredder alive going "well, until we solve the Riemann Hypothesis, we'll neven know if that answer has an impact on what I'm doing... and I guess we'll never really know if what I'm doing is wrong or not".
You can also use the consciousness argument to defend anything, "Is stealing a blue car wrong? We would need to really drill down and figure out the fundamental aspects of consciousness and if they are any different for a person driving a blue car versus any other color." This is not a great argument. Again, you can always move the goalposts to justify your action under the pretense that "you can't prove that I'm wrong".