There's an old story (possibly apocryphal) about a scholar who went to a university and presented a paper on telepathy. The study had been well-designed, the results collected by impartial researchers, and the results significant. On the basis of these results, the scholar argued, there were good reasons to believe in some telepathic capacities. The listeners to the talk smiled and nodded, asked polite questions, and then ended early. Frustrated, the telepathy researcher turned to a scholar in the audience and said, "none of you believe me. But the evidence is right there! Why don't you accept it?" The scholar smiled and responded, "if your theory is true, then everything else we know would need to be false."
A number of integrated information theory of consciousness (ITT) folks of late have felt a bit like the telepathy researcher. They feel like their theory is science-y enough: it involves lots of math, has axioms, makes (sometimes eccentric) predictions. But people have generally dismissed it as kooky, dismissing it out of hand--or, as recently, when the only results on offer for the theory were either inconsistent (e.g., values of Phi) or generic and compatible with any theory (COGITATE), as no longer seriously in contention. It must seem unfair: after all, IIT supporters have evidence, too! Why don't people take the evidence as seriously as they do?
I don't like the term "pseudoscience," but I do like the phrase, "tribunal of experience." The idea behind it is that we don't evaluate evidence, a hypothesis, or even a whole theory on its own terms, independent of the rest of our beliefs. We instead force it to answer to the totality of our beliefs. A theory of telepathy has to contend with the overwhelming success of our understanding of physics, biology, neuroscience, and psychology--all of which provide ample reasons to regard telepathy as mere spooky action at a distance. As such, it is simply too silly to take seriously.
I'm more sensitive to this than most because I grew up in a conservative environment and dabbled in young Earth creationism as a kid. This is a kind of "pocket theory," taking small bits of evidence which call into doubt this or that aspect of evolution. But, if true, it would need to overturn huge bodies of theory, from astrophysics to geology. Our whole scientific edifice would need to be false if young Earth creationism is true. And that makes it obvious why evolutionists didn't take it seriously and didn't need to argue against me when I'd spout off weird facts about this or that. From their perspective, the burden of evidence faced by a creationist like me is overwhelming. If they call into question this or that minute fact, who cares? It doesn't even begin to speak to the totality of evidence we've acquired from the rest of the natural sciences.
IIT is a pocket theory. It aims to provide a theory of consciousness that will be evaluated "on its own merits," independent of everything else we know about philosophy, biology, psychology, and neuroscience. But that's not a real option for science. Any scientific theory is constrained by all the other domains which form the tribunal of scientific experience. And against that mountain of evidence, the confusing and inconsistent results regarding Phi and the bizarre predictions about conscious plants and pantheism are just silly.
Which is where the "pseudoscience" charge comes from. The label--right or wrong--is really an expression for a kind of exasperation. It says, "you're coming at this wrong. You can't start your theory beginning with introspection. Introspection is more controversial and less certain than all the stuff we know from the other sciences. You are required to start with the other sciences; they are the most immovable stuff we've got." The problem with IIT isn't that the results are controversial or counterintuitive; it is that these controversial and counterintuitive results demand at the start that we ignore the rest of what we know about the material world. The starting point is, given what else we know, absurd.
This is why people like me just shake our heads at IIT (or, for that matter, most non-physicalist theories of consciousness which appeal to introspection). I don't know what consciousness is, but everything else science tells us is that it'll be a physical process that brains evolved that provided some adaptive advantage. This suggests introspection, while providing some uses and advantages, probably is not so interesting that we should reconsider the foundations of natural science.
I don't need to know what the right theory of consciousness is to have a general sense of what it needs to look like, since I already have a good sense of what other mental processes--such as early vision or auditory processing--look like. The eventual theory of consciousness will look like that, just some function brains do, without anything spooky or magical about it. It'll probably not even seem that interesting, when all is said and done. But a good theory isn't about satisfying our intuitions; it is about fitting into our comprehensive understanding about how everything--in the broadest sense of the term--hangs together with everything else.