Paul knew how his statements sounded
As with Jewish society, 1st century Greco-Roman society contained a wide range of attitudes towards women, from the misogynist to the egalitarian.
From this socio-historical background, we know that private associations were free to decide on their own codes of conduct even if these breached social norms,  and that 1st century Christian women (whether Jews or Gentiles), would have had reasonable expectations of participating in the congregational worship as a result of their previous religious experiences.
Egalitarian scholars have noted this particular feature of Paul’s commandments, in the seven passages in which he gives commandments concerning the relationship of men and women in the ecclesia and the family using a formulated style.
1 Corinthians 11:3-16:
* Commandment: Women’s heads should be covered when praying and prophesying
* Reason: The woman is the glory of the man, woman came from man, woman was created for man, and because of the angels
* Mitigation: In the Lord woman is not independent of man, nor is man independent of woman; just as woman came from man, so man comes through woman, but all things come from God
1 Corinthians 14:34-35:
* Commandment: Women should be silent in the ecclesias, they are not permitted to speak
* Reason: Let them be in submission, as the Law says; it is disgraceful for a woman to speak in church
* Mitigation: If they want to find out about something, they should ask their husbands at home
* Commandment: Wives, submit to your husbands
* Reason: The husband is the head of the wife
* Mitigation: Husbands, love your wives and do not be embittered against them
* Commandment: Wives, submit to your husbands
* Reason: It is fitting in the Lord
* Mitigation: Husbands, love your wives as Christ loved the ecclesia
1 Timothy 2:8-15:
* Commandment: Women must learn in all submissiveness; I do not permit a woman to teach or to hold authority over a man, she must remain quiet
* Reason: Adam was formed first, and then Eve, and Adam was not deceived but the woman, being deceived, fell into transgression
* Mitigation: She will be delivered through ‘childbearing’, if she continues in faith and love and holiness with self-control
* Commandment: Wives are to be subject to their own husbands
* Reason: So that the message of God is not discredited
* Mitigation: [not explicit]
All these passages contain instructions concerning the role and relationship of women in the ecclesia and in the family which Paul knew would be seen by women themselves as placing limits on their participation in the ecclesia and placing them under the authority of their husbands, and which he sought to soften in some way as a result.
Four of these passages appeal explicitly to other passages of Scripture for support, and none are explained as a response to an existing local situation, nor justified as just a cultural accommodation.
 ‘But studies of Roman society have found a variety of indicators about the status of women, and what was true about women in the eastern part of the empire was not necessarily true about women in the western empire. On the one hand, there was the household headed by the husband/father/master, a hierarchical order-obedience structure that included those who were economically dependent. On the other hand, there were emancipatory ideas about women that allowed them greater freedom and economic independence (some were even the heads of households).’, Tanzer (egalitarian), ‘Eph 5:22-33 Wives (and Husbands) Exhorted’, in Meyers, Craven, & Kraemer, ‘Women in scripture: a dictionary of named and unnamed women in the Hebrew Bible, the Apocryphal/Deuterocanonical Books, and the New Testament‘, p. 481 (2001).
 ‘Whereas in the larger outside world, both Roman control and residual customs mitigated against mixing men and women, slave and free, foreign and religious practice; in the voluntary associations there was a lively atmosphere in which these mixes could be tried out and experienced without threat of larger social catastrophe or consequences.’, Nerney, & Taussig, ‘Re-imaging life together in America: a new gospel of community‘, p. 12 (2002).
 ‘a “mitigation,” “softening of the blow,” or “saving phrase” to make the statement, assertion, or command less offensive to women.’, Walker, (egalitarian) ‘The “Theology of Woman’s Place” And the “Paulinist” Tradition’, Semeia, p. 106 (28.1983).
 ‘In 11:11–12, however, he backtracks lest the Corinthians become confused and think that he implies that women are inferior to men. He is not attempting to establish a gender hierarchy that places women in a subordinate role. Since he argues from hierarchy to make his case about head coverings, he needs to caution against any misapplication of what he says. Women and men are interdependent in the Lord.’, Garland (egalitarian), ‘1 Corinthians’, Baker Exegetical Commentary on the New Testament, pp. 508-509 (2003).
 ‘In other contexts, among some gentiles, Paul’s moral conservatism and reaffirmation of traditional roles for women would have appeared too confining (this appears to have been the case in Corinth).’, Witherington (egalitarian), ‘Women’, Anchor Yale Bible Dictionary, volume 6, p. 959 (1996).
 ‘a. General Statement, Assertion, or Command (vv 8–12) I desire then that in every place the men should pray, lifting holy hands without anger or quarreling; also that women should adorn themselves modestly and sensibly in seemly apparel, not with braided hair or gold or pearls or costly attire but by good deeds, as befits women who profess religion. Let a woman learn in silence with all submissiveness. I permit no woman to teach or have authority over men; she is to keep silent. b. Reason or Justification (vv 13–14) For Adam was formed first, then Eve; and Adam was not deceived, but the woman was deceived and became a transgressor. c. Mitigation, Softening of the Blow, or Saving Phrase (v 15) Yet woman will be saved through bearing children, if they continue in faith and love and holiness, with modesty.’’, Walker, (egalitarian) ‘The “Theology of Woman’s Place” And the “Paulinist” Tradition’, Semeia, p. 197 (28.1983).
 ‘In some passages, the pattern becomes more complex, and, at times, it is not clear whether element “c” is present at all. Thus, the pattern of 1 Pet 3:1–6 is ‘a’ (v 1a), ‘b’ (vv 1b–2), ‘a’ (vv 3–4a), ‘b’ (vv 4b–6a), with v 6b either a continuation of ‘b’ or perhaps a very subtle form of ‘c.’ The pattern of 1 Cor 14:34–35 is ‘a’ (v 34a), ‘b’ (v 34b), ‘a’ (v 34c), ‘b’ (v 34d), ‘a’ or possibly a subtle form of ‘c’ (v 35a),16 ‘b’ (v 35b). In Titus 2:4–5, the pattern is a simple ‘a’ (vv 4–5a), ‘b’ (v 5b), with ‘c’ absent altogether. Three of the passages introduce a somewhat modified form of element ‘c’ with a command to husbands that they love their wives. Thus, Col 3:18–19 follows the simple pattern, ‘a’ (v 18a), ‘b’ (v 18b), ‘c’ (v 19), while Eph 5:22–33 has the more complex pattern, ‘a’ (v 22), ‘b’ (v 23), ‘a’ (v 24), ‘c’ (vv 25–33a), ‘a’ (v 33b); and 1 Pet 3:1–7 has the pattern, ‘a’ (v 1a), ‘b’ (vv 1b–2), ‘a’ (vv 3–4a), ‘b’ (vv 4b–6 or perhaps 4b–6a with 6b a very very subtle form of ‘c’), ‘c’ (v 7). The analysis of 1 Cor 11:3–16 is again complicated by the question of the unity of the passage.17 If it is a single unit, then the pattern is apparently ‘a’ (vv 3–6), ‘b’ (vv 7–10), ‘c’ (vv 11–12), ‘b’ (vv 13–16), although the distinctions are not as clear here as they are elsewhere. If, however, the passage is divided into three pericopes, as has been suggested, then the following patterns emerge: “Pericope A” follows the pattern, ‘a’ (v 3), ‘b’ (vv 8–9), ‘c’ (vv 11–12); “Pericope B” the pattern, ‘a’ (vv 4–6), ‘b’ (vv 7,10,13,16), with no ‘c’; and “Pericope C” consists almost entirely of element ‘b,’ with ‘a’ only implied and ‘c’ absent altogether.18’, ibid., p. 107.
 The precise meaning of the Greek word here is a matter of interpretation; the majority of commentators understand it as a figure of speech for the role of the woman as wife and mother, sometimes as ‘motherhood’, such as EDNT, ‘According to 1 Tim 2:15 in its interpretation of Gen 3:16, bearing children / motherhood is the special task of women, including according to v. 15b a life in faith (possibly a reference to the rearing of children in faith; cf. b. Ber. 17a): σωθήσεται δὲ διὰ τῆς τεκνογονίας.’, Balz & Schneider, ‘Exegetical dictionary of the New Testament. Translation of: Exegetisches Worterbuch zum Neuen Testamen’, volume 3, p. 340 (1990-c1993), and ANLEX, ‘bearing children, childbearing, motherhood (1T 2.15)’, Friberg, Friberg, & Miller ‘Analytical lexicon of the Greek New Testament’, volume 4, p. 376 (2000); ‘The final interpretation may be termed “the majority view.” 44 This view would hold that Christian women are not saved through teaching and asserting authority, but by attention to their traditional role. “Childbearing” serves as a figure of speech to illustrate Paul’s argument that women need not behave as men but rather fulfill their divinely appointed role to find salvation.’, Moss (complementarian), ‘1, 2 Timothy & Titus’, The College Press NIV Commentary (1994).
 1 Corinthians 11:7-9; 14:34, 1 Timothy 2:13-14, 1 Peter 3:5-6.
 The commandment in Titus 2:5 for wives to submit to their husbands is justified here by ‘So that the message of God is not discredited’, but the same commandment is also accompanied by two additional reasons elsewhere; Ephesians 5:23, ‘The husband is the head of the wife’, Colossians 3:18, ‘It is fitting in the Lord’.