After telling Timothy to pray for leaders that we might lead a peaceable life so the gospel can reach “all men” (2:1-4), Paul tells him it his will that “therefore” he pray “every where,” since all men are found everywhere.
You can pray lifting up your hands if you want to (v.8 cf. Ps.141:2), but when Paul talks about lifting up “holy hands,” some think he was thinking of how under the law God didn’t answer prayer if your hands weren’t holy (Isa.1:15; Ps.66:18). Under the law you also couldn’t pray with “wrath” (v.8 cf. Mark 11:25) or “doubting” (v.8 cf. Mark 11:23,24). But we’re not under law (Rom.6:15), so Paul’s not thinking of all that.
In the context of praying for leaders in government, if men aren’t lifting up holy hands it might be because their hands are involved in unholy activities like resisting the government they are supposed to submit to (Rom.13:1-8). They shouldn’t be full of “wrath” against them, “doubting” their leadership. That’s how the Greek word for “doubting” is often used. The 12 doubted the leadership of one another, thinking they could lead better (Mark 9:33,34). Paul also used that Greek word when he said that we should receive weak brethren but not to doubtful disputations (Ro.14:1). Some men accept the leadership of leaders but are always second-guessing them.
Paul isn’t changing the subject when he begins speaking about “women” (2:9). Married women also have a leader whose leadership they are tempted to question and second-guess, thinking they could lead the marriage better than their husband. This is something they should pray about “in like manner” instead of being wrathful about.
The first way a woman accepts the leadership of her husband is by dressing “modestly” (v.8 cf. Pr.7:10) “with shamefacedness,” a lack of being restrained by shame. “Sobriety” means making good decisions while dressing, unlike the bad decisions women make when they are drunk. “Broided” or braided hair was associated with immodesty back then but it isn’t now. But if there’s nothing wrong with wearing gold (Gen.24:53) or pearls or costly array (Ezek.16:10-13), why’s Paul say that there is? Well, Peter couldn’t have been saying he was against the “putting on of apparel” (IPe.3:3) in general, he must have been against excesses in putting on apparel and gold. The Greek word for “adorning” he used (3:3) is elsewhere always translated “world,” so he’s saying if a woman’s whole world revolves around her adorning it’s a problem. By the way, the Greek word is kosmos, from which we get cosmetics. A woman’s’ cosmetics should be “a meek and quiet spirit” and “good works” (2:9cf.Eph.2:10), specially the “good works” women excel at (ITim.5:10).
“Silence” (2:11) can’t mean total silence (Acts 21:40; 22: 2), but if it did, that was probably a custom then, not now, like how they wore hats instead of rings to show they were married (ICor.11:1-11). “Subjection” (2:11) doesn’t mean inferiority (Lu. 2:51), but it does mean a woman can’t teach men (2:12). They can teach children like Timothy himself (IITim.2:5 cf. 3:15) and other women (cf.Tit.2:2,3) for that isn’t usurping or seizing authority that belongs to a man.
Paul says women shouldn’t lead men since they were designed to be followers not leaders (2:13). In addition to being second in creation they were first in the fall (v.14) because they are more easily deceived, as when Solomon’s mother didn’t know giving his brother David’s wife to his older brother would give him a claim to the throne (IKi.2: 17-22 cf. IISam.12:7,8). Paul knew women are more easily deceived doctrinally as well (IICor.11:3), and Satan loves it when women become pastors, get deceived, and lead others in deception.
A woman can’t lead men but they can bear children and lead them (2:15). Women naturally “desire” to rule their husbands (Gen.3:16), but their part of the curse is that he must override this desire and rule them (cf.Gen.4:7). Of course, these women who started on the right path by choosing to have children must “continue” on the right path (2:15) by ruling their children well, or they’ll become unruly and she’ll return to wanting to rule her husband.