For certain senses of the word "why" in that sentence, which do not "explain away" the experience, there might not be more to explain.

From reading Dennett, I have not yet got the sense that he, at least, ever means to answer "why" non-trivially. Trivially, I already know why I insist - it's because I have subjective experience. I can sit here in silence all day and experience all kinds of non-verbal assurances that this is so - textures, tastes, colors, shapes, spacial relationships, sounds, etc.

Whatever systems in my brain register these, and register the registering, interact with the systems that produce beliefs, speech, and so forth. What I'm looking for, and what I suspect a lot of people who posit a "hard problem" are really looking for, is more detail on how the registration works.

Dennett's "multiple drafts" model might be a good start, for all I know, but it leaves me wanting more. Not wanting a so-called Cartesian Theater - just wanting more explanation of the sort that might be very vaguely analogous to how an electromagnetic speaker produces sound waves. Frankly, I find it very difficult even to think of a proper analogy. At any rate, I'm happy to wait until someone figures it out, but in the meantime I object to philosophies that imply there is nothing left to figure out.