Me [Rachel]: “This person says the men in my life need to do a better job of exercising their God-ordained authority to ‘silence’ me.”
Dan [her husband]: “You tell him that this man’s doing everything in his power to make sure your voice is heard.”
First, the opposite of the popular feminism Rachel has bought into is complementarianism, not a misogynistic patriarchy, as I have argued here before that both pop-feminism and abusive patriarchy are different expressions of misogyny. Only complementarianism seeks to exalt the woman as a woman rather than discarding womanhood in order that she might be more acceptable (i.e., more like men in their roles).
Second to this, the commands in Scripture for the woman to be in submission to the man or to be silent in regard to instructing men are given to the woman to carry out, not to the man. Look at them below:
Wives , submit yourself to your own husbands, as to the Lord. For the husband is the head of the wife, as Christ also is the head of the church, He Himself [being] the Savior of the body. But as the church is subject to Christ, so also the wives are to submit themselves to their husbands in everything. (Eph 5:22-24)
Wives, be subject to your husbands, as is fitting in the Lord. (Col 3:18)
In the same way, you wives, be submissive to your own husbands so that even if any [of them] are disobedient to the word, they may be won without a word by the behavior of their wives, as they observe your chaste and respectful behavior. (1 Pet 3:1-2)
The first thing we notice is that the command is given to wives, not to husbands. That should be the first clue that this isn't something that husbands are to do, but what wives are to do.
The second thing we notice is that, in light of the above, the voice is likely be understood as a middle, i.e., "submit/subject yourself."
The third thing we notice (if I had further quoted the passages) is that the husband's role is to love his wife by patiently teaching her, seeking her holiness and goodness, and refraining from anything that would harm her physically and spiritually. He governs her growth and shepherds her. His job isn't to try and silence her in some forced manner, but perhaps it would be to instruct her if what she was saying was obnoxious and unbecoming of Christ and His truth. He is her teacher after all, but he is not her disciplinarian or tyrannical dictator.
Now, concerning the passages where the church does not allow a woman to teach, it's important to note that first it is still talking about what a woman needs to do, not what men make her do. However, the elders, who are men, don't allow her to teach, and that is an exercise of external authority with which a woman might disagree. But the elders have authority over what teaching is done, whether that concerns men or women, and so they are exercising ecclesiastical authority to preserve the order of the church in the immediate. They can't wait for a person to get it. And, of course, to be in rebellion against the church leadership, when they represent Christ accurately, is to rebel against Christ Himself. But even this isn't forced. They are simply commands that the woman needs to submit herself, not commands for the leadership to force her to submit herself. It may be that if she continues to rebel and teach others to be rebellious toward God and His order that she needs to be placed under church discipline, as any man would be, and eventually set out of the church; but again, that is something true for every man who is self-willed and not taking the glory of God and the whole of the community as more important than himself.
Finally, even the expression of God that the man must govern the woman in Genesis 3:16, although it is something the man needs to do, is said to the woman, as if to say to her that this is something she needs to seek from him if chaos is to be thwarted (interestingly enough, this is the argument we are given in 1 Timothy, i.e., that the chaos of heresy and apostasy can be thwarted if the order of creation and the Scripture is in place in the church).
And let's be real honest for a moment. I'm not sure I could ever make my wife do something she really didn't want to do. That would likely be a battle of epic proportions. This image of poor helpless women trapped in complementarian marriages doesn't exist. Those are women trapped within abusive patriarchy, not complementarian marriages. The reason why I say that is that pretty much every single woman I have met who is a complementarian is a strong-willed woman. Did you get that? And they have to be, because their views aren't mainstream. They're constantly living counterculturally, so they have to be tough. They've also all come to their positions themselves, not by force from their husbands. In fact, a forced complementarianism is a contradiction in terms, as the man is not to make the wife submit in complementarian thought, but instead to teach her and nurture her into what is good (although 9 times out of 10 she already knows what she needs to know) and allow her to come to the right of it on her own. I realize this is anecdotal, but pretty much every woman I know who believes in real complementarianism, who is truly a woman of the Word who knows what it really is and what it requires of her is not a weak little woman under the shadow of her overbearing husband who is constantly trying to silence her. Indeed, I have hardly known men as strong as these women, so enough with the nonsense, and let's deal with the reality that we have multiple groups here, not two (i.e., the abusively controlling and the supportive nurturers).