I think the fact that Adam's sin is what plunged the human race into a sin nature (1 Corinthians 15:22) is clear evidence that patriarchy existed before the curse. Remember that Eve sinned first not Adam. If Adam had not been the one "in charge" then Eve's sin would have brought the curse not Adam's.
All of that hinges on what you mean by "patriarchy", a word that means different things to different people. There are certainly inferences that can be drawn from Paul's exposition that "by one man sin entered the world" or that "in Adam all die", but what's "clear" from that can be fussed about. Anyway, it's not the main point here.
So while Genesis 3:16 clearly indicates something changed with regard to a husbands ruling (my hypothesis is this change is because of the fact that he now has to deal with her sin nature) I don't believe that is where it started...
Nor do I believe that ruling her is "being the curse of God in her life." (yes a new thread might be good)
Let's talk about the "something" that changed, since that's the whole point. I would say 'separate thread', but the same sort of finagling is going on here that is going on with Eph 5, so I figure it's relevant.
God tells Eve three things: (1) He'll greatly multiply her sorrow and her childbirth, making childbirth a sorrow to her (seems obvious enough what that means), (2) her desire shall be to her husband (whatever that means), and (3) her husband shall rule over her (whatever that means). It seems pretty clear (without the baggage of 'needing' this verse to say anything in particular) that there is a difference between (1) on the one hand and (2) and (3) on the other.
In the first matter, God says He is going to "greatly increase" something, so it seems plain that Eve was already able to have children and had some reason to know or anticipate what childbirth was like. It's required for God's language in His judgment to make sense. If Eve were unequipped to have children before the fall, the language would have been completely different.
In the same way, both the second and third matter are simple changes of state, not an increase or decrease in the quality or quantity of something. This is going to happen, and that's going to happen. Implying that they weren't already happening, or else implying that God speaks in meaningless tautologies just because He can. "Your desire will be to your husband, and he will rule over you." These are new things that haven't been happening yet.
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If the "something" you're avoiding referring to is some sort of change in the manner or severity of his "rule", one would expect God to have said "and he will rule over you with a rod of iron" or some such appropriate figure of speech, but that's not what He says. The "something" that changed is that
now he's going to rule over you. Shouldn't have eaten that apple. Shouldn't have listened to that snake. Shouldn't have been talking with snakes in the first place.
So as a result of disobeying God and Adam, Eve is going to be
under the rule of her husband. That's what the text says, and coincidentally that's what it means.
None of this has anything to do with Eph 5, except that the same mistake is being made in both cases. Don't make the text say something it doesn't say, just accept what it
does say and work with that.
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Note that even this passage is not a
command to husbands to rule over their wives, any more than "wives, submit to your husbands" is. Pacman, you suggest that rule is required because of the woman's (new) sin nature, but it could just as easily be something defective about the post-fall man. Maybe fallen man is going to spend the rest of time running the woman into the ground to make up for that one time he let her call the shots. Who knows? All we know from the text is that as a simple statement of fact, God tells the woman that from now on she's going to frustrated in her relationship with her husband, and will no longer enjoy the intimate oneness she enjoyed pre-fall. The big question is whether Christ's blood and the indwelling Holy Spirit change any of that, at least if we're doing it right.
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Note further that God doesn't command the man to keep the woman in check, or even suggest that that is his primary duty; God focuses on the bitter futility of the work the man will do from now on. Notice the 'chain of command' thing going on there, the symmetry? God gave man work to do (tending a garden, animal husbandry, etc), and henceforth that work is going to be a drag. God gave woman work to do (assisting the man in his work and bearing his children), and henceforth that work is going to be a drag. The big question is still whether Christ's blood and the indwelling Holy Spirit change any of that, at least if we're doing it right.