Right, so an eliminativist would reply that our intuitions about the meaning of words and thoughts are only ways of being misled. The eliminativist uses language to communicate facts that are supposed to be understood in a counterintuitive way, as something like a set of meaningless causes and effects.
So eliminativism has mystical as well as nihilistic implications. It's like how the Buddhist asks us to conceive of a world in which the individual self or ego doesn't really exist. It requires a gestalt switch.
I've spoken to Scott Bakker at length about this and wrote some articles for his blog, so I think I have a good grasp of how the eliminativist would argue.