https://en.wikipedia.org/wiki/Hard_problem_of_consciousness
I think the underlying issue here is the limitations of human understanding. There are really only two possibilities here. One is that human knowledge can come to understand everything, as in absolute mysticism where the mind merges with all of reality. As to why it takes absolute mysticism, it's because the various finitudes we experience are greatly interconnected, and so if you are going to abolish one, the others need to go, too.
The other position is that human understanding is always limited. I and many other philosophers in the last century or so (such Neitzsche, Husserl, Heidegger, Merleau-Ponty, Whitehead, the later Wittgenstein, Strawson, and all the Pragmatists) believe that human beings, as finite, mortal creatures, are inherently finite in their understanding, and so there will always be mystery.
As to where the dividing line lays, I think the hard question of consciousness is one topic on the other side. One good argument here comes from Colin Mcginn, who says that the human brain is not designed to answer this sort of question.
What you refer to as 'conscious experience' is an emergent property of processes in the brain in communication with one another. The 'subjective aspect' is an internal recreation of the external world, continuously updated from data provided through the senses. Ergo, no need to go invoking some invisible undetectable subatomic substance, the phlogiston of the mind.
