What is wrong with the pot calling the kettle black?

We hear this pseudo-refutation in debate all the time. It implies that the speaker is a hypocrite. Instead of refuting the claim, it in essence seeks to shut the speaker up. But the fact that the pot may indeed be black doesn’t change the truth of its charge that the kettle is black as well. Why don’t we insist that the kettle answer the charge instead of trying to belittle its accuser into silence?

Let’s take a real-world example. An alcoholic, totally familiar with the signs of alcoholism, tells someone they are a fellow alcoholic. Does the charge lose all merit because the one making it is himself guilty? Isn’t it just as true when he says it as it would be if someone who had never imbibed in their whole lives leveled the accusation?