OP, an update post explaining for anyone interested.
Dialectic is not a formula. The products of dialectics cannot be given before dialectical treatment of a subject matter itself is gone through. Dialectic is not a set of presupposed or assumed axiomatic laws about reality or thought. Dialectic is literally what it says: sustained analytic dialogue within a subject; dialogue of a peculiar kind for it is not a dialogue between persons. To state it more clearly: dialectic is the relentless analysis and critique of concepts only according to the content of the concepts themselves in a long running internal dialogue in the content of the concept. The relentless analysis of concepts happens to show that no concept has meaning on its own, its content includes its other, its dialectical opposite. This unity of opposites is not a law of dialectic itself, it is a provable result of dialectic carried out. Dialectic happens to show that all concepts will break down under relentless analysis and find themselves groundless in-themselves, finding the resolution of their failures in other concepts which themselves will eventually fall. The negation of the negation happens to be true for every concept you can conceive from apples to gender. All ideas are incapable of standing on their own and either dissolve in skepticism or find themselves as a specific rule to another concept.
Hegel’s dialectic was the analysis of pure concepts, his Logic focusing on ultimately the analysis of what a concept is in-itself, and culminating in an Absolute Idea, an ontological concept whose content is the entire Logic which provides the concept of what it means to be absolute. Being leads to Nothing because the content of Being is Nothing. Nothing leads to Being because Nothing is not. Being finds itself Becoming Nothing, and Nothing Becoming Being. Becoming is the higher concept which contains what appeared to be a logical contradiction of two opposite concepts being each other’s content, i.e. Becoming is the sublation of Being and Nothing, the concept which contains them and is itself more than they are yet maintains Being and Nothing as its real content. This simple analysis is a dialectical analysis carried out. This process of analysis is dialectics. Being and Nothing are dialectically related because each necessarily contains the other in their own content, just as capitalist and worker contain each other in the content of their concept.