I really like Augustine, but the following is just terrible biblical exegesis:
What was said to Cain about sin, or the perverted desire of the flesh, is said in this passage about the sinful woman, and here is to be taken as meaning that man, in ruling his wife, should resemble the mind which rules the flesh. For that reason the Apostle says, 'A man who loves his wife is loving himself. For no one ever hated his own flesh.' [Augustine, City of God, XV.7, Henry Bettensen translation, 1972 Penguin edition]
The sense of 'flesh' Paul has in mind in Ephesians 5:28 is not the same sense as when he speaks of the flesh as something to resist. He's talking about people loving their own flesh as a good thing and thus a model for how a husband treats a wife. How can it follow from that that a husband would rule over his wife the way my mind might rule over my flesh in the bad sense of 'flesh'?
This is an obstacle complementarians face in recognizing distinction of gender roles but equality of nature. That kind of relationship isn't master-slave but can nonetheless have an authority structure. Augustine's view of a husband-wife relationship isn't standard complementarianism today, and it's not the view that I think the biblical passages on this assume. Complementarians tend to place themselves in a mediating position between Augustine and absolute egalitarianism, which calls any gender role distinctions evil.
Egalitarians naturally resist that characterization, since calling a position mediating suggests that other views are extreme. But such resistance shouldn't justify mischaracterizing another's view. We should seek accuracy in representing how relate to each other, and I've seen countless attempts by egalitarians to place contemporary complementarian positions such as those of D.A. Carson, Thomas Schreiner, William Mounce, Craig Blomberg, or Bruce Waltke on the same level as what Augustine says. Those who really do know what complementarians are saying who do this are making the difference between Augustine and contemporary complementarianism out to be nothing, and that strikes me as deliberate misrepresentation. Advocating ultimate husband leadership in a marriage but with significant input and even major decision-making on the part of the wife will in practice look far more like an egalitarian marriage than like the master-slave model that many egalitarians portray complementarianism as advocating. Even those who will still disagree with complementarianism ought to acknowledge that, and I see much egalitarian rhetoric as trying to cover over such distinctions rather than acknowledging them.