Easy. Zombies are just not a thinkable concept. We cannot really conceive of them, we have no "clear and distinct" idea of what a zombie is.There is the crux of it all. How does one refute the claim that zombies are possible without it looking to a neutral person like there has been an assumption of the conclusion.
We can say that we know very well what a zombie is, it is a thing exactly like a human but with no mind, but that is just repeating the definition. Do we understand the definition and if we don't then how do we know that the definition makes sense?
When we try to imagine a zombie we first imagine a human being, in front of us, behaving exactly like an ordinary conscious human does. And then we say the words ".. but he has no consciousness". How exactly is that last step anything other than just words? How do we imagine his lack of consciousness?
The zombie idea presupposes that consciousness is undetectable from the outside. So we are not imagining actually seeing a lack of consciousness in our zombie. Nor can we be imagining putting ourselves in the zombie's place and discovering that we have no consciousness - this would just be silly. If we are imagining anything here we are just imagining the existence of a rule which says that imagining ourselves in this person's place is an invalid thing to do and that's what makes him a zombie. But this is just a rule about how we must behave towards him. We haven't actually imagined anything about him that sets him apart from a conscious human.