It was no sophomoric error when Friedrich Engels described Aristotle — not Plato or some neoplatonist — as the greatest dialectician of the ancient world.
Broad usage of the term “dialectic” includes meanings of both dialogue and logic. For Plato, dialogue aimed directly at truth (though not necessarily reaching it). Aristotle considered a many-sided logical/semantic analysis to be the single most important tool of science, and to be more rigorous than the dialogue that was Plato’s favorite literary device.
For Aristotle, unlike Plato, dialectic is not a direct quest for truth. It is instead an inferential/semantic examination of opinion or what is merely said (or, I would argue, of appearance). It uses the same logical forms as the rational knowledge Aristotle called episteme; but unlike the latter, yields results that Aristotle calls only “probable”, because they depend on premises that are merely “said” rather than rationally known. (This is a qualitative assessment having nothing to do with statistical probability.) This has often been taken as a denigration of dialectic. I take it instead as an affirmation of the importance of semantics. (Plato would already emphasize that dialectic is a matter of an ethically motivated quest for truth rather than a claim to mastery or simple possession of it. Aristotle opens things up further by preferring an indirect, semantically oriented approach to the quest.)
Aristotle also says (Topics Book 1) that dialectic in just this “merely probable” sense is the best means we have for getting clarity about first principles. Aristotle’s own approach to what later came to be called “metaphysics” is (“merely”) dialectical in a specifically Aristotelian sense. In being so, it is essentially semantic and normative. I don’t think Aristotle regarded metaphysics as episteme (“science”) any more than he regarded ethics or phronesis (“practical judgment”) as episteme, and in neither case is it a denigration. (Aristotle is far more honest than most later writers about the relatively less certain nature of so-called first principles, compared with many other apparently more derivative results. He is the original antifoundationalist. See also Abstract and Concrete.)
Hegel actually said the greatest example of ancient dialectic was the commentary on Plato’s Parmenides by neoplatonist Proclus (412 – 485 CE). (He did not know the work of the other great late Neoplatonist, Damascius (458 – 538), which included an even more sophisticated development along similar lines.) The Parmenides explicitly examines a series of antithetical propositions, which does resemble the common image of Hegelian dialectic. (See The One?) In any case, I think this is misleading.
While at least the common image of Hegelian dialectic as concerned with antitheses does not apply well to Aristotle, very fruitful clarifications of Hegel can be obtained by looking out for his use of Aristotelian-style dialectic, despite that fact he — general enthusiasm for Aristotle notwithstanding — did not much mention Aristotle when expounding his own version. Underlying the occasional emphasis on antitheses in Hegel is a broader concern for actually many-sided inferential/semantic examination of opinion or appearance, which is just what Aristotle’s dialectic does. (See also Aristotelian and Hegelian Dialectic; Three Logical Moments; Contradiction vs Polarity.)
My own candidate for the greatest example of ancient dialectic is the development of the concepts of ousia (“what it was to have been” a thing) and energeia (“at-work-ness”) in the central books of Aristotle’s Metaphysics. As in the biological works, merely binary distinction is not the main point there.
The stereotype of a binary schematism at work in Hegel is not without basis, but more careful commentary has limited its scope. Aristotelian dialectic actually pervades Hegel’s works.
In a dialectical development (Aristotelian or Hegelian), it is common to begin with one presumed meaning for a term, and end up with a different one. The classic discussion in the Metaphysics mentioned above begins with the idea of a simple substrate that remains constant through a change, and goes through multiple transformations to progressively richer concepts. (See also Aristotelian Demonstration.)