First, it seems impossible to imagine that the quale for red and the quale for green could ever be the same as long as we can distinguish red and green. So, we can never intuitively reduce red to green, or, indeed, reduce one quale to another. (This suggests to me that we should identify a quale for X with "a capacity to recognize X". However, I don't need to adhere to such a controversial statement.)
My second observation is that when things are said to "reduce" in the sciences, that reduction never reduces one quale to another. I'll describe what I mean with a specific example.
NOTE: As a preface to my example about reduction, let no one persist in the faulty belief that reductionism is eliminative. Reduction of water to H2O does not eliminate water, nor does it eliminate oceans, droplets or any other watery things. Reduction identifies, but does not eliminate. Reduction identifies a droplet of water with a configuration of H2O molecules. At the end of the reduction process, droplets of water still exist.Suppose we reduce a droplet of water to the presence and motions of H2O molecules. What does this mean in terms of qualia?
Well, the reduction relies on experiments. Things like electrolysis which breaks water into oxygen and hydrogen gases, spectroscopic experiments the can identify the gases by the light they absorb, and the way hydrogen burning in oxygen creates water vapor.
However, at no time can we say that the qualia we experience while performing the experiments are equivalent to the experience of, say, dipping our hands in a pond. If they were equivalent, then we would be unable to distinguish the experience of performing the experiments (and perhaps the experience of making the relevant inferences) from the experience of dipping our hands into a pond. That would be absurd.
Yet I doubt that any of us is uncertain that water reduces to H2O. We don't think that water is anything more than H2O. We don't argue that there is some non-physical stuff which bridges the gap between the qualia of our experiments and the qualia of water itself.
The conclusion is that reduction does not equate qualia. Reduction is about ontology.
What is ontology? Ontology looks at all of our experiences and asks what is the minimum number of substances and relationships that explain those experiences. When we see an apple, we don't assume that every property of every apple, and every possible conjunction of properties, at every moment in time is ontologically basic. There is something it is like to gaze at the same apple for 10 minutes, and there is something it is like to glance at the apple, and these two qualia are distinct. But we don't think that gazed-at apples are ontologically different from glanced-at apples. We think there is just one apple, whether we gaze at it, glance at it, look at its silhouette, or take a bite of it.
Ontology seeks to reduce the vast multitude of our experiences down to the fewest number of causes. In this case, a single apple, seen from different perspectives.
So, let's return to qualia in the mind-body problem. The goal of the Knowledge Argument, for example, is to show that the quale for red does not reduce to a scientific, ontological model. This seems to me to be a doomed project. Reduction never equates one quale with another. The fact that reduction doesn't do this (ever) is not a mark against reductionism. I now think that these sorts of arguments confuse epistemological basics with ontology.
Qualia are the most basic of epistemological inputs, and these inputs are unique. Ontologies are epistemological outputs. Epistemological outputs are never equivalent to basic epistemological inputs (because epistemological outputs are distinguishable from the things they model). Ontologies can, at best, explain or predict relationships between epistemological inputs.
Where does this lead us?
There's an implicit assumption in dualist arguments that, if minds were physical, they ought to be able to do what we cannot. This is an implicit assumption because, if we believed that physical machines could not reduce one quale into another (i.e., that they would be in the same position that we are in), then we could not conclude that we are non-physical from the position we are in! Every mind would be in that position, whether physical or not!
So, would physical minds be in the same position?
Assume that a physical mind can exist and be conscious. This mind is going to have some raw experiences, some raw recognitions, some distinguishable inputs. When this mind works out an ontological model of its world, the best it will be able to do is to correlate the epistemological basics of its experience (its inputs), and build a model. That model may predict its inputs perfectly, but the model is not the same thing as the input it is predicting. If it were the same thing as the input it were predicting, then the model would be indistinguishable from what it was modeling.
I conclude that a physical mind will find itself in exactly the position in which we humans find ourselves. The only way the machine won't be that way is if it is incapable of distinguishing simulations of its model from the real thing. Again, this seems absurd.
Having shown that physical minds will be in the same position in which we find ourselves, I can argue that we can't infer ontological dualism from the position in which we find ourselves. The inability to reduce one quale into another is not a feature of dualist minds but of all minds, including purely physical ones.