If your account of the subject treats it as an object, you are leaving something out. But it’s hard to avoid doing this when we make the subject the soul or soul-action, a faculty, a “thinking thing”, the monad, a homunculus or “self” that is at the levers of the body, a brain or brain portion or modular interaction or feedback loop, etc. Even if these things were realities they would not explain subjectivity in its opposition to objectivity. The “discovery of the subject” in Modern philosophy progressed by an interior logic to the point where we had to confront the radical opposition of the subject to the object, which was confronted in Medieval times as the opposition between the intentional and the entitative. Even then, however, there is a drag in such discussions that tend to play down or forget about the opposition. There is a tendency in the mind to monism: metaphysicians and scientists both sink towards understanding all being as object.