“No you” is actually a valid point in a disagreement
Not the exact wording but the general premise behind it is a fair counter point in any disagreement. When someone is attempting to gain a higher moral authority, bringing up any hypocrisy is a reasonable thing to do. If pointing out hypocrisy is then dismissed, it is reasonable to assume the other person is not arguing in good faith and therefore should no be taken seriously.
This has a name, "Tu Quoque" and it is, in fact, a logical fallacy.
If someone calls you out for kicking puppies, it is not a fair counterpoint to say that they kick puppies too. Their actions are immaterial to your actions. If the question is one of morality, your actions are immoral regardless of whether or not your accuser is similarly immoral.
I disagree for one that it is “in fact” a logical fallacy and also that their actions are immaterial to your actions. To make that counterpoint I would have had to have been aware that the person calling out my puppy kicking did in fact kick puppies. You can not say this knowledge is immaterial.
While you can still conclude that my puppy kicking is immoral it does not serve any purpose because the criticism came from someone equally immoral. I could even argue (if true) that I’m only kicking puppies because I saw them doing it and I didn’t know it was immoral.
“No you” is similar to “don’t throw stones in glass houses” and is a reasonable point.
I disagree for one that it is “in fact” a logical fallacy and also that their actions are immaterial to your actions.
You're free to disagree, but it doesn't change that you're wrong. If the argument is that your puppy kicking is immoral, it is a fact that your accuser's actions are immaterial. (Obviously we are presupposing that we agree what is immoral, and that puppy kicking fits that understanding.)
Assume there is Person A or Person B, the first kicks puppies, the second does not. Your argument holds that your puppy kicking would be immoral if Person B accused you, but somehow not immoral if Person A accuses you. That's obviously not the case; therefore, person A's actions are immaterial.
Tu Quoque is a fallacy because it does not actually address the argument made, it is a form of ad hominem attack. Given a valid argument, true premises will necessarily lead to a true conclusion. Fallacious arguments are not valid in structure; therefore you can't know if your conclusion is true.
It's considered a formal fallacy. That doesn't mean it's necessarily a bad point in context, it just isn't the point it's often presented as. If someone is making a long speech about how X is bad, when they do it themselves all the time, then you're probably right to discount their arguments - if they're not stupid, they're dishonest. But pointing out the hypocrisy is technically "off topic" if you're arguing whether X is actually bad.
Also, only really works if they are "attempting to gain a higher moral authority" (as OP says). As if that's the only reason people would argue a point. I think it says something about OP that they take that as a given for arguments. I can immediately imagine scenarios that one can argue against a thing that they themselves participate in.
"Hey, smoking is bad, kid. Don't do it."
"But you smoke! And I look so cool with a cigarette!"
"Yeah, it's a habit that's very difficult to break and it makes your life worse in every way. I know from experience."
"No you."
But I agree with your main point,
But pointing out the hypocrisy is technically “off topic” if you’re arguing whether X is actually bad.
It's considered a fallacy exactly for this reason. When you're debating a thing, you're way off the map if you think that's your winning move if you're arguing in good faith. An argument should be about showing your point is correct, not that you're better than the other person. But Mr. Wang up there may only view arguments as a competition to be won morally.
You cannot square these two statements. If it's a fallacy then you are not justified in discounting their argument. They may be a hypocrite, but it doesn't mean that their argument isn't both valid and sound. The smoking example by the other reply is a great example.
Wrong, you absolutely can. It's considered a fallacy, logically or formally speaking, because it doesn't deal with the actual "point", but casts aspersions on whomever's motives or fitness to deliver it. If you are strictly debating Topic X then that is technically (or logically, or whatever) irrelevant. In reality, if someone is moralizing at you then their being immoral or amoral is actually pretty significant.
If any given person is saying [something you're doing] is morally wrong, then you'd be naturally less inclined to take that feedback from e.g. Hitler. I hope. Formally that is an error, in reality it's still sort of a reasonable thing to keep in mind.
Yes the argument I’m making is about if it is appropriate for the person to be arguing in the first place without considering their own hypocrisy, not whether x is actually bad so I see what you mean about it being off topic. It’s like them saying everyone leaves their shopping cart in the parking lot and it’s bad but when I do it it’s ok, their point about it being ok when they do it is irrelevant, it’s still bad.
Very often it's not exactly the same criticism, and is just deflection - they are hoping to start arguing about whether the accuser's actions are equivalent, rather than whether their actions are objectively bad.
For example: A accuses B of allowing poor people to starve to death and B replies that if A cares so much about poor people, why does he want to put taxes up?
I do agree that your example is deflection although it is not an example I would describe as not exactly the same. While it has some similarities it is not close enough to exact to be described that way.
Pointing out hypocrisy can be relevant, but often is just whataboutism. It is perfectly valid to have different opinions on similar situations, because no two situations are completely equivalent.
That said, anyone arguing in good faith should be prepared to examine their own biases as well - as long as they really are relevant to the latter at hand.
I see a few different ways this could play out, and it highly depends on the specifics of the point being debated. Fundamentally though, pointing out hypocrisy is a good way to criticise the speaker, but it does nothing to refute the point that they are making. It's a form of ad hominem argument—a term which, contrary to how it's sometimes used, doesn't just mean "insulting your interlocutor", it specifically means that your argument doesn't address their point, but merely addresses the person making it.
It could be that they simply didn't realise they're being hypocritical. You explaining it might make them realise the breadth of the argument they were making and cause them to reevaluate and realise that the implications of what they were saying were more severe than they previously thought. You haven't actually addressed their argument, but you didn't need to. Your goal was to help them realise for themselves that it was wrong. They then update their belief in line with this. (Which, depending on the specifics of the argument, and whether or not they and you are both acting in good faith, might mean the end up completely abandoning the point, or simply redrawing the precise boundaries of the point, or something else.)
It could be that they realise, and it's something they either don't care about, or do care about but don't see it as refuting their argument. For example, in an argument about addiction, an addict might recognise their addiction and be working on overcoming it, or just be living with it. You pointing out that they're addicted to [whatever it is] doesn't really advance the argument at all. Either they're trying to work on it, or maybe they've acknowledged their addiction but don't really care. Whatever the case may be, how sound their point is is not affected by this quality of them.
I think it’s a litmus test for if the person is arguing in good faith or criticising with the goal of moral superiority. If a concession can be given by the person being critical after “no you” this shows the criticism really is out of concern and want for improvement rather than simply satisfying the criticisers own indignation.