The p-zombie theory holds that being able to conceive of something makes it possible; and because p-zombies are possible, therefore dualism. The tricky bit appears to be "conceive of" in a sense that implies possibility. Consider these statements:

1. I can conceive of 2+2=4 being true in conventional Peano arithmetic.
2. I can conceive of 2+2=5 being true in conventional Peano arithmetic.
3. I can conceive of P being equal to NP.
4. I can conceive of P not being equal to NP.
5. I can conceive of p-zombies, therefore dualism.
6. If I can conceive of p-zombies then dualism, which is a confused idea, therefore p-zombies is a confused idea by reductio ad absurdum.

With the second, I am claiming to "conceive of" something trivially false. I arguably haven't conceived of anything actually possible; I've just shuffled some words together.

With the third and fourth, I'm claiming to have conceived of something no-one knows (though many suspect 3 is false and 4 is true). To what extent have I actually thought it through? At some point I will hit a contradiction with one of them, though no-one has yet. Both are "conceivable" in some sense; certainly that they've formed a sentence in their head that they can try out for its logical implications. But one of those statements is as wrong as 2+2=5 nevertheless.

When someone claims that p-zombies are a conceivable thing at all, and that they have conceived of them, this doesn't actually say anything about the world or what is even possible; it just says they've formed a sentence in their head they think they can try out for its logical implications. But try telling them this. (I have, and haven't managed a sufficiently robust form of 6. to be convincing.)

(I still consider the fundamental argument in favour of dualism is that its advocates really want it to be true, and that p-zombies is like creationism for smart people.)