Update: Upon reflection, I'm not entirely satisfied with this post. I think I definitely managed to identify some of the confusion around these kinds of discussion, but a smaller proportion than I would have liked.
The Zombie argument (David Chalmer's website, Stanford Encyclopedia of Philosophy) is one of the most famous arguments against materialism, so I'll assume that you can find an explanation yourself if you aren't already familiar with it.
I always find it fascinating when you have two sides that can't seem to communicate with or understand one another. I think the root of the problem is that both sides have a different notion of what counts as a zombie. The Dualist Conception of consciousness involves qualia, so their conception of a philosophical zombie is an entity that lacks qualia. This is a notoriously hard term to define - some would say because it is meaningless - but all that matters here is that they have a stricter conception of consciousness that the Materialist. The Materialist Conception of consciousness involves certain processes taking place, so a Materialist Conception of a zombie would involve certain processes taking place, but also not taking place, which would be a contradiction.
Here's the confusion. If a someone were to claim that humans don't fit the Dualist Conception of a zombie and that Materialism is true, they'd be contradicting themselves, because Dualists have a wide conception of what counts as a zombie that all entities in a Materialist world would fit this definition. On the other hand, if someone were to claim that that Materialist Conception of a zombie were logically possible, which is merely to claim that they can posit this without contradiction, they would be mistaken since Materialist's have such a narrow conception of what would count as a zombie that this class is an empty set.
Once the definition of what counts as a zombie has been fixed, so too has the outcome of the argument. And this is really contingent on what counts as consciousness, so the Zombie argument isn't actually where the fundamental difference lies. This isn't a mere linguistic difference, it's a question of what natural structures exist that cry out to be given a label. Or as Richard Kennaway might frame it, an attempt to understand the nature of a phenomenon which we already have some experience with, without foreclosing the possibility that we might end up tossing away the concept if we find it confused.
One last clarification: many people find this argument persuasive. In so far as this is the case, it's usually because they had an inconsistency in their thoughts. For example, perhaps they identified as materialists, without thinking through exactly what a materialist view of consciousness would entail, and when they realised this, they discovered it was something that they didn't endorse.