The Tug of Intuition, Or, Intuition as Reason Smasher

I keep thinking about the role of intuition in our thought processes. Here's a passage from a recent NYTimes piece discussing two thought experiments about whether or not consciousness can be accounted for in a physical way.:

The logical possibility of a zombie-twin strikes most people as intuitively obvious: what could there be in my overall physical make-up that logically requires that I be conscious? (Even Daniel Dennett, who in the end denies the possibility of zombies, has noted the powerful “tug” of the idea and admits, “I can feel the tug as well as anybody.”)

Presumably the "tug" Dennett talks about is the tug of his intuition, which is at odds with the explicit reasoning he develops in the case. Where does that intuition come from? – that's what interests me. The point of such thought experiments seems to be to send such intuitions crashing into explicit reasoning that is to the contrary.
Here's an old post about intuition, and another one. Here's my own comments on those thought experiments. Perhaps I'll say a bit more about intuition in this context.