Making use of an argument about a subject X, Person 1 presents his view to Person 2. Then Person 2, who is against that position, simply makes the following claim: "Hey dude, you have committed the fallacy Y, so you're wrong!". Period. He doesn't explain why the Person 1's claim is a fallacy. So, let's suppose it's a fallacy, but a not very known fallacy. My question is: In this case, isn't Person 2 committing a fallacy too, when he affirms that Person 1's claim is a fallacy without explaining why? If so, which fallacy is he committing?
There are in fact two things going wrong here:
- Person 2 claims that person 1 used a fallacy, but doesn't tell why. This is not a fallacy, as a fallacy only occurs in arguments, but there's no argument here - there's only a statement.
- Person 2 claims that because person 1's argument is fallacious, therefore the conclusion must be wrong. This is called Argument from fallacy.
It depends whether the second person is engaging in a discussion whether a statement is true or false, or not.
If A says "the statement X is true because ... " and B says "you are committing fallacy Y", then the argument whether X is true or false is undecided; you could actually say that A might have made the better points so far.
But if B is highly experienced, and doesn't really care what A says, and usually is right in his claims, then A is better off checking his arguments. B isn't committing any fallacy, because B isn't really arguing with A. Unless we have the rare case that B is wrong this time, B might just be a little unhelpful.
In such a situation A might assume that B hasn't really refuted the claim X at all, but might be able to refute A's argument anytime he or she wishes. It would be very embarrassing if A tried to show his argument to C, and then B pops up saying "I told you that you are committing a fallacy and you didn't change any of your argument. So here is what the fallacy is, why it is a fallacy, and why X is actually wrong".
They could be engaging in The Burden of Proof Fallacy. Then again, they might not.
Given how frustrating it is to keep talking about Person 1 and Person 2, I am going to name them traditional names, without loss of generality: Alice and Bob. It simply makes the rest of the argument easier to read.
The real question would be in how Bob expects his rejection to be taken. Usually its not that someone like Bob thinks merely naming a fallacy is enough to reject an argument. They usually assume that, once pointed out, even the original speaker could work through the fallacy themselves.
If Alice can deduce the fallacy in her own argument, then no second fallacy has occurred. What has occurred is simple efficiency of rhetoric. Why say a paragraph when a sentence will do?
However, if Alice cannot agree with the claim that her argument has a fallacy, then Bob's behavior will decide whether a fallacy has occurred. If Bob responds by taking the time to walk Alice through his argument, then no fallacy has occurred. Bob just tried to be efficient, and had to back up to defend it.
If Bob blows off Alice, then Bob has indeed committed a fallacy himself, assuming that "just because I made a statement assumes it is proven."