“The man is the head of the woman”
The crucial text for strengthening this interpretation, or at least for rendering it plausible, is arguably 1 Corinthians 11:1–16—“in the same letter he raged on and on about hairstyles in the assembly.”  In this passage, on my reading, Paul makes practically explicit the ratio between the politics of the spirit and the politics of the body. The crucial verses are 3, 7–9, and 11–12:
I would have you know, however, that every man's head is Christ, but a woman's head is the man, and Christ's head is God. (11:3)
For a man must not veil his head, since he is the image and reflection of God but a woman is the reflection of man. For man did not originate from woman, but woman from man. Neither was man created for woman's sake, but woman for man's. (11:7–9)
Of course, in the Lord there is neither woman without man nor man without woman. For just as woman originated from man, so, too, man exists through woman. But everything comes from God. (11:11–12)
These verses have been much discussed from many points of view. It is far beyond the scope of the present chapter to analyze either the theological or hermeneutic issues involved in the text, but however we interpret them, it is clear that Paul explicitly thematizes two (partially opposed) forms of conceptualizing gender, one in which there is an explicit hierarchy and one in which there is none. Paul himself marks this difference (the gap between the hierarchy of verses 7–9 and the “there is neither woman without man nor man without woman” of verse 11) as the situation of “in the Lord” (ἐν κυρίῳ). I do not think it is going too far—nor is it unprecedented in Pauline interpretation—to connect this “in the Lord” with the “in Christ” of Galatians 3:28 and read both passages as a representation of an androgyny that exists on the level of the spirit, however much hierarchy subsists and needs to subsist in the flesh, in the life of society even in Christian communities. These two levels might well correspond, indeed, to the two myths of the origins of the sexes as found in Genesis 1 and 2. The no-male-or-female, which is “in the Lord,” or “in Christ,” would represent the androgyne of chapter 1, understood, as in Philo, as neither male nor female, while the “since he is the image and reflection of God, but a woman is the reflection of man. For man did not originate from woman, but woman from man,” which Paul cites here, would be a reference to the story as found in chapter 2! “In the Lord” might even be seen then as an allusion to “in the image of God,” and the latter human of chapter 2 would be “in the flesh” in contrast. This perhaps speculative interpretation is dramatically strengthened if Josef Kürzinger's suggestion is accepted that verse 11 means, “In the Lord woman is not different from man nor man from woman” (Kürzinger 1978). Ultimately, as Karen King suggests, the two myths of gender “are quite compatible in that both imagine the ideal to be a unitary self, whether male or androgynous, whose nature is grounded in an ontology of transcendence and an epistemology of origins.” 
These verses demonstrate that Paul had not changed his mind or backslid from Galatians; they also explain, given the context of the Corinthian correspondence, why he chose to omit “There is no male and female” in the Corinthian version of the baptism. I suggest, therefore, that for Paul just as much as for the Corinthians, a state of androgyny, a cancellation of gender and sexuality, would have been the ideal. The difference between them lies in the application of the principle. The Corinthians believe that they have already achieved a state of perfection that permits the acting out of the cancellation of gender difference, whereas Paul is skeptical of their achievements (cf. 4:8). This does not, however, imply that for Paul the ideal of androgyny has no social consequences.
There are in fact three (not mutually exclusive) options for a social enactment of the myth of the primal androgyne. Some gnostics (and perhaps the Corinthians) seem to have held that once having attained the spirit, humans transcended gender entirely and forever whether in celibacy or libertinage. Philo, on the other hand, restricts such transcending redemption from gender to celibates, and then only to special ritualized moments of ecstasy. Paul's strictures against women with short hair and the speaking out of women prophets (14:37–38)—if the latter is genuinely Pauline—seem to suggest a third option: For all (not only celibates) there is no male and female, but only momentarily in the ritualized ecstasy of baptism. It is only then, in this life, that people attain the status of life in the spirit, in Christ or in the Lord, in which there is no male and female. Another way of saying this is that Paul holds that ontologically—according to the spirit—there is a permanent change in the status of gender at baptism, but insofar as people are still living in their unredeemed bodies, gender transcendence is not yet fully realized on the social level—according to the flesh. Perhaps, we might say, that final realization awaits the Parousia. I am thus inclined to agree with Tertullian's view that the notion of Paul giving celibate women the power to teach, preach, and baptize that is functional, social equivalence to men seems hard to credit. On the other hand, it may not be gainsaid that he had women associates in his ministry, nor that he implied that virgins could achieve spiritual states unavailable to the married (7:32–35). All three of these possibilities are equally dependent, however, on a notion that gender difference exists only at one ontological level, the outer or physical, the corporeal, but that at the level of true existence, the spiritual, there is no gender, that is, they depend on dualism. Much of the immediate post-Pauline tradition seems to have adopted a version of the first option—namely, that celibate women could attain a permanent state of the erasure of gender, a development that has had profound effects on the later discourse of gender in European culture.