Abnormality is a serious problem for a philosophy that grounds objectivity and truth on intersubjective reality, as does Husserl's phenomenological philosophy. (Let me boil this down. In Husserl's view, I think, there's objective empirical science, and truth, because there is a world that is universally real for all people. That means, in short, that our actions always being motivated by and directed toward that same world. In turn, there is such a world because, between us, our community, our communication, and our being human is based on our being with one another and recognizing one another as human. So, the very fundamental basis of objectivity and truth is our being interconnected and sharing this common world of experience.)
If there's abnormality, as Husserl says himself in the texts collected in Husserliana XXXIX -- Die Lebenswelt [The Lifeworld] -- there seems to be contradiction within this common, universal world. In that case, its unity, and hence its universality, would seem to fail. Now, if that fails, so to does the ultimate warrant of addressing objectivity or truth.
Husserl addresses this in terms of there being normal and abnormal experience. His example in text number 16 of Die Lebenswelt is about the normality of color-sightedness and the abnormality of color-blindness. They each deal with the world in terms of their own way of seeing, even though this seems to mean the world they share in common harbors a contradiction. Husserl's extremely dissatisfying answer, in this text, is, that they acknowledge that each sees the same world, the same things, but differently. Oooooo-kay, but this isn't really resolving anything. His examples are so general that they're superficial, almost meaningless.
This matters to me as an intriguing philosophical question. But it matters more as a practical problem in the world. I'll get at this two ways, one through more academic philosophy, the other through everyday life.
I now read almost all philosophy through Jean-François Lyotard's book The Postmodern Condition (1978). In this book, Lyotard asserts that the current state of knowledge is characterized by "incredulity toward metanarratives" that serve to give warrant to the discourses that generate knowledge. In effect, his claim is that the connection between reality itself and the discourses that claim to tell us about reality is one that is now doubtful. Physics, for instance, used to be grounded in a claim either to be able to present the whole truth about the reality of bodies in motion, or to be able to make life better for us by making nature our servant. Neither of those are claims that physics can make for itself, because they aren't claims about bodies in motion, but claims about what the study of bodies in motion can do. So, they are not scientific knowledge claims, but narrative knowledge claims -- stories about the role of physics in the world. But those stories are no longer credible, the first because physics itself has led to the discovery of the limits of objective knowledge in physics (viz. Heisenberg), the second because physics has allowed us to build bombs that threaten to blow up the world and all the physicists with it.
Here's why, in everyday life, this matters. In the postmodern condition of incredulity toward metanarratives, we have technological apparatus of scientific knowledge, including all the stuff we make out of it, but without the grounding of those claims on a reality principle. So, we live in a world of competing and contradictory claims about reality. The simplest example of this is the "debate" over global climate change. In this debate, there are 97% or so of people with backgrounds in science discourses, who all agree that there is global climate change, that it is a problem, and that human activity contributes to this change. Then there are 60% or so of US Republicans, who do not believe in global climate change, regardless of their backgrounds. Rich members of this latter group fund "research" institutions that generate "knowledge" that climate change is not real, or not significant, or not caused by human action, or not a problem, or caused by trees, etc. (I note in passing the lovely Democritean skepticism of this argument. It's like Metrodorus' On Nature: there is no global warming; if there is, we can't know anything about it; if we can know anything about it, it's not important; etc.)
Under the postmodern condition, with the connection between knowledge-generating discourses and reality severed, these competing, contradictory knowledge claims co-exist, but their co-existence is untenable. They cannot both be correct. (This is assuming that the climate change detractors are not cynically pursuing profit, which is certainly possible.) It matters very much who is right, and so it matters very much that we have some way of addressing this contradiction.
We don't. We vote on it, which is as absurd as voting on whether the things we perceive have color or not. Reality being intersubjectively grounded does not mean we vote on what's real. It means that there is a reality, a universal world, to which we can all refer for adjudicating our differences, and toward which each of us is directed, and in reference to which a perspective is normal or abnormal. Or else.
And so far, Husserl's response to this major problem is, yeah, we deal.