Egalitarian writers often claim that male headship did not come about until after the Fall, and is, accordingly, a consequence of the Fall.

Gilbert Bilezikian (Beyond Sexual Roles) writes of Adam and Eve:

Instead of meeting her desire and providing a mutually supportive and nurturing family environment, he will rule over her.… The clearest implication of this statement [Gen. 3:16], conferring rulership to Adam as a result of the fall, is that he was not Eve’s ruler prior to the fall.

And Rebecca Groothuis says:

In fact, there is no mention of either spouse ruling over the other—until after their fall into sin, when God declares to the woman that “he will rule over you” (3:16). This is stated by God not as a command, but as a consequence of their sin.

Wayne Grudem outlines the following points by way of response:

1. The order: Adam was created first, then Eve (note the sequence in Genesis 2:7 and 2:18-23; 1 Timothy 2:13).
2. The representation: Adam, not Eve, had a special role in representing the human race (1 Corinthians 15:22, 45-49; Romans 5:12-21).
3. The naming of woman: Adam named Eve; Eve did not name Adam (Genesis 2:23).
4. The naming of the human race: God named the human race “Man,” not “Woman” (Genesis 5:2).
5. The primary accountability: God called Adam to account first after the Fall (Genesis 3:9).
6. The purpose: Eve was created as a helper for Adam, not Adam as a helper for Eve (Genesis 2:18; 1 Corinthians 11:9).
7. The conflict: The curse brought a distortion of previous roles, not the introduction of new roles (Genesis 3:16).
8. The restoration: Salvation in Christ in the New Testament reaffirms the creation order (Colossians 3:18-19).
9. The mystery: Marriage from the beginning of creation was a picture of the relationship between Christ and the church (Ephesians 5:32-33).
10. The parallel with the Trinity: The equality, differences, and unity between men and women reflect the equality, differences, and unity in the Trinity (1 Corinthians 11:3).

Grudem, Wayne. Countering the Claims of Evangelical Feminism (p. 72). The Crown Publishing Group. Kindle Edition.

It should be noted that Kevin Giles (What the Bible Actually Teaches on Women) argues at length against such ‘inferences’.  (His target is not Grudem directly, but the Kostenbergers, God’s Design for Man and Woman).  Giles urges that Genesis 1 ‘unambiguously’ teaches that man and woman ‘have the same status, dignity, and authority’, and that there is nothing in chapter 2 that would contradict this.  In my view, Giles’ work is characterised by misrepresentation of the work of those he opposes, and of misplaced confidence in his own interpretations.