I would consider that a new argument (if it wasn't mentioned until the rebuttals) and would disregard, however some judges would probably accept it.
I don't understand how you can justify your position. How can you not
accept a K in the rebuttals? If I use vulgarity in my 1NR, the aff can't K me for it in the 1AR? If I endorse genocide in my 1NR, the aff can't K me on it in the 1AR? I mean, how can you disregard an argument like that just because it was new in the first rebuttals?
If you use vulgarity, I will reflect that in your speaker points and speak to tournament officials about your unprofessionalism.
If you endorse genocide in your 1NR, and hadn't brought that up in your constructives, I will disregard it.
The purpose of rebuttals is to clarify and extend existing arguments, which were built in the constructives. You are supposed to be "rebutting," or answering existing arguments, not forming new ones. There is meant to be a difference between constructive and rebuttal speeches -- hence the names.
1. But you won't give the loss based on a K that the aff brings up? (something that would clearly be permissible during the constructives)
2. You're going to disregard an endorsement of genocide?
3. Perhaps the names should be loosened. The purpose of the constructive-rebuttal format is to engender a deep, thoughtful debate. I don't see how that goal is furthered if the aff is not allowed to K the neg in the 1AR for something said in the block. By allowing it, it brings the proper issues into the forefront of the round.
Take another example: The independent voter for fairness. My 1NR says aff can't bring new responses because of xyz. Aff brings new responses. I run the independent voter. New argument? Yep. Never argued it until the 2NR. But is it legit? Absolutely. No other way to run it.
The "no new arguments in the rebuttals" is an already in-place metastructure. Politely asking the judge to disregard a new argument is not a new argument in itself. In your example, your 1NR is referring to metadebate guidelines. Your 2NR response to AFF's mistake is not a new argument. Their blunder, however, merits no more than a quick mention to the judge (why you are not going to spend time responding) and then you should move on. By spending large amounts of time on that issue, you lose the opportunity to respond to the arguments which have been laid out in the constructives.
If you picture the debate round as a building project, the teams lay a foundation together in the constructives. In the rebuttals, the walls, windows, doors, etc are built on that existing foundation. I as a judge will ignore extra buildings whose foundation was laid in the rebuttals. I am expecting a deep and thoughtful debate - not one where last-minute arguments are thrown out without time for either team to extend or answer. New arguments in the rebuttals do not allow for that deep and thoughtful debate; that is the whole purpose behind the metastructure restriction.
Also, you need to be sure ou have a clarity on the difference between an "argument" and a supporting point to an existing argument. An argument is a line of reasoning in itself, which can be rebutted either by refuting a premise (or supporting statement) or by showing that the premises do not lead to the conclusion. Once the main arguments are presented in the constructives, continued discussion of those arguments (including adding supporting premises and answering them) is permissable in the rebuttals. What teams may not do is begin a whole new line of argumentation.
Let me see if I can give a simplified version to show what I mean:
Aff argues that:
c1. Dogs are loyal
c2. Dogs are trustworthy
c3. Cats are neither loyal nor trustworthy
So, c4. Dogs are superior pets to cats.
c1. Cats can be loyal.
c2. There is more to being a superior pet than loyalty & trustworthiness; the amount of work required by the owner is also a factor in superiority of pet choice. In the rebuttals
r1. Dogs are not always trustworthy (refers back to Aff c2)
r2. Cats require less work on the owner's part than dogs, so cats are superior pets (refers back to Neg c2)
r1. Dogs are more loyal than cats; cat loyalty examples are rare, but dog loyalty examples are common (refers to Aff c1&c3, and Neg c1)
r2. Amount of owner work is a part of pet superiority, but dogs actually require less work than cats (refers to Neg c2, and Neg r2)
r3. More people own dogs than cats, so that shows they are superior (NEW argument, does not refer to any constructive premise/conclusion; judge will disregard whether true or false
Does that make sense?