Arguments against qualia typically challenge the very coherence of anything which could play the desired role. It's not like trying to prove fire doesn't exist, it's like trying to prove there is no such thing as elan vital or chakras.
I think there's some hindsight bias there, in the case of chakras. It is by no means obvious that these supposed centres of something-or-other distributed along the spine and in the head don't exist. One might be sceptical purely on account of the sources of the concept being mystical or religious, but the same is true of meditation, which has been favourably spoken of by rationalists. It's only by actually looking for structures in the places where the chakras are supposed to be and not finding anything that could correspond to them that the idea can be discarded. There is also (I think) the fact that different traditions assert different sets of chakras.
"Élan vital" was always a fake explanation for a phenomenon -- life -- that no-one understood. It's like a doctor listening to a patient's symptoms and solemnly making a diagnosis by repeating the symptoms back to the patient in medical Latin. No-one talks about élan vital now because the subject matter succumbed to investigation based on "stuff is made of atoms".
But consciousness is different -- we experience it. We have no explanation for it, just the experience -- the fact that there is such a thing as experience. "Consciousness", "sensation", "experience", "qualia", and so on are not explanations, just names for the phenomenon.
So clearly there is such a thing as subjective experience, in some sense. This, however, is not what is at issue.
To me, this is exactly what is at issue. We have subjective experience, yet we have no idea how there can possibly be such a thing. All discussions of this, it seems to me, immediately veer off into people on one side putting up explanations of what it is, and people on the other knocking them down. The fact of experience remains, ignored by the warring parties.
It seems to me the best case for exponents of consciousness is to force a dilemma - an argument pushing us on the one hand to accept the existence of something which on the other appears to be incoherent (as per just above).
There is no case to be made. Either you have this experience or you do not. I have it and I think that most people do. What people -- at least, those who do have subjective experience -- need to do first is recognise that there is a problem:
I have subjective experience.
It is impossible for there to be any such thing as subjective experience.
All of the argument is about proposed solutions to this problem. But refuting every solution to a problem does not solve the problem.
Weisberg et al. (2008) presented subjects with two explanations for psychological phenomena (e.g. attentional blink). Some subjects got the regular explanation, and other subjects got the 'with neuroscience' explanation that included purposely irrelevant verbiage saying that "brain scans indicate" some part of the brain already known to be involved in that psychological process caused the process to occur.
And yet, Yale cognitive science students rated the 'with neuroscience' explanations as more satisfying than the regular explanations.
Why? The purposely irrelevant neuroscience verbiage could only be important to the explanation if somebody thought that perhaps it's not the brain that was producing certain psychological phenomena. But these are Yale cognitive science students. Somehow I suspect people who chose to study cognition as information processing are less likely than average to believe the mind runs on magic. But then, why would they be additionally persuaded by information suggesting only that the brain causes psychological phenomena?
In another study, McCabe & Castel (2008) showed subjects fictional articles summarizing scientific results and including either no image, a brain scan image, or a bar graph. Subjects were asked to rate the soundness of scientific reasoning in the article, and they gave the highest ratings when the article included a brain scan image. But why should this be?
I remember talking to a friend about free will. She was a long-time physicalist who liked reading about physics and neuroscience for fun, but she didn't read Less Wrong and she thought she had contra-causal (libertarian) free will.
"Okay," I said. "So the brain is made of atoms, and atoms move according to deterministic physical law, right?"
"Right," she said.
"Okay. Now, think about the physical state of the entire universe one moment before you decided to say "Right" instead of something else, or instead of just nodding your head. If all those atoms, including the atoms in your brain, have to move to their next spot according to physical law, then could you have said anything else than what you did say in the next moment?" (Neither of us understood many-worlds yet, so you can assume we're talking about a single Everett branch.)
She paused. "Huh. I'll have to think about that."
"Also, have you heard about those studies where brain scans told researchers what the subjects were going to do before the subjects consciously decided what they were going to do?"
"No! Are you serious?"
"Yup. Sometimes they could predict the subject's choice 10 seconds before the subject consciously 'made' the choice."
"10 seconds? Wow. I didn't know that."
I think that maybe the 'with neuroscience' explanations and brain scan images are more satisfying partly because they remind us we're physicalists. They remind us that reductionism marches on, that psychology is produced by physical neurons we can take pictures of.
Just like most people, physicalists walk around all day with the subjective experience of a 'unity of consciousness' and contra-causal free will and so on. If a physicalist isn't a researcher who studies all the latest successful reductions in neuroscience or biology or physics all week long, and doesn't read Less Wrong every day, then it's possible to get lost in the feel of everyday experience and thus be surprised by a headline like 'Brain Scanners Can See Your Decisions Before You Make Them.'
Sometimes even physicalists need to be reminded — with concrete reductionistic details — that they are physicalists. Otherwise their normal human anti-reductionistic intuitions may creep back in of their own accord. That's one reason it helps to study many sciences, so you have many successful reductions in your head, and see (at some resolution) the entire picture, from psychology to atoms. As Eliezer wrote:
To her credit, my friend no longer believes in contra-causal free will.