Unpopular Opinion

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.