Nagel’s difficulty is essentially this: he believes that there are some experiences which are completely beyond human understanding.
We might, he argues, imagine an approximation of what it might be like if we were bats. It is possible to imagine being nearsighted, eating bugs, hanging upside-down in an attic, and perhaps even flapping our arms to fly. But this is just what it is like for US to be a bat… not what it is like for a BAT to be a bat.
A similar analogue might be drawn for a person who was blind from birth. They might develop an intellectual understanding of what light is and learn about how sighted people react and use it, but Nagel suspects that even with all the training in the world, they will never really understand what it is like to SEE.
This is the kind of subjective experience that he identifies with with consciousness itself. And he takes great pains to observe that although we can do a great job describing how neurons work, we still have essentially no explanation for consciousness itself. We can describe any number of phenomenon associated with thinking beings, but in any of them consciousness seems to be something that might be there or not… we don’t even have a way to definitively tell whether other humans are conscious, though they certainly seem to be.
His argument, then, is that although science seems able to objectively describe things in such a way that no point of view is necessary or even implied, it should also acknowledge the presence of this ineffable subjective experience as well. He doesn’t suggest that such experience is necessarily beyond the bounds of analysis. Quite the contrary – he seems mostly to be advocating a greater study of it; that the whole is perhaps greater than the sum of its parts.