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.
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,
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.