The primacy of Subject in a suitably non-dual mode is essentially the idea that consciousness in some larger sense goes all the way down to the very root of things, that what is opened or brought to light or truth in experiencing, or Dasein, is original being. Opposed to this would be a view say of consciousness or as emergent out of some massively complex rule based network structure of elements whose being is a pure positing, and so a sophisticated metaphysics. The problem with the former view would seem to be that it can only clumsily account for the persistence at all levels of complex networks such as the brain and whatever underlies subatomic physics etc. The problem with the latter is that it cuts off any deep connection between reality and truth, or equivalently that it leaves the inner nature of being, which is the being of beings, entirely dark. That these two views seem to exclude each other is a limitation of understanding. It's not a synthesis but a unification that is needed by pushing each to its respective extreme.