I do not permit a woman to teach or to exercise authority over a man; rather, she is to remain quiet.
1 Timothy 2:12 NKJV
You should have also noticed that I started out by saying that "I often wonder about this" and then proceeded to point directly to the first three words.
And, I guess you can claim a win by pointing out those two words I slipped in, "To me" but let's just say we can leave those words out and my point is still the same.
Similarly, here's an example from Scripture of women teaching and even correcting a man. Where in Scripture are they reprimanded for doing this?
Now a Jew named Apollos, a native of Alexandria, came to Ephesus. He was an eloquent man, competent in the Scriptures. He had been instructed in the way of the Lord. And being fervent in spirit, he spoke and taught accurately the things concerning Jesus, though he knew only the baptism of John. He began to speak boldly in the synagogue, but when Priscilla and Aquila heard him, they took him aside and explained to him the way of God more accurately.
Act 18:24-26 NKJV
Now, you are opening a huge subject upon which I have pondered within the Bible for decades. I'll try to summarize the biblical teachings. I go back to the beginning. The principle that God is teaching us in Genesis 1:26-27 and Genesis 2 is that God created male and female equal in STATUS before him (Genesis 1:27) but with different ROLES or functions in their relationship with each other (Genesis 2:20).
Gen 1:26 Then God said, “Let us make man in our image, after our likeness. And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth.”
Gen 1:27 So God created man in his own image, in the image of God he created him; male and female he created them.
Gen 2:19 Now out of the ground the LORD God had formed every beast of the field and every bird of the heavens and brought them to the man to see what he would call them. And whatever the man called every living creature, that was its name.
Gen 2:20 The man gave names to all livestock and to the birds of the heavens and to every beast of the field. But for Adam there was not found a helper fit for him.
We can see by comparing Genesis 1:26 and 2:20 that the "dominion" of humans over the animal world fell to Adam as the leader in terms of his relationship with Eve, since she wasn't created yet when he had the responsibility to name them, an action that showed that he had authority over them.
Then, in verse 23, Adam names her "woman" (Ishah) with an ending on his name (Ish) before they fell into sin. After their descent into sinful rebellion, he names her Eve (Genesis 2:20) because of the curse that meant male dominance (Genesis 3:16).
Gen 3:16 To the woman, he said, “I will surely multiply your pain in childbearing; in pain you shall bring forth children. Your desire shall be contrary to your husband, but he shall rule over you.”
Gen 3:20 The man called his wife's name Eve, because she was the mother of all living.
Therefore, male leadership is NOT male dominance but is servant leadership, as Paul also says in Ephesians 5:22-27. In marriage, the husband's responsibilities are to serve all his wife's needs the way Jesus serves the church's needs. She must "submit" him as the "head," as the church also must to Christ. We must use the Bible's meanings, not our own, of its words. "Submit" means to voluntarily give in to someone's servant leadership, whereas "head" is clearly a servant-leader.
Eph 5:22 Wives, submit to your own husbands, as to the Lord.
Eph 5:23 For the husband is the head of the wife even as Christ is the head of the church, his body, and is himself its Savior.
Eph 5:24 Now as the church submits to Christ, so also wives should submit in everything to their husbands.
Eph 5:25 Husbands, love your wives, as Christ loved the church and gave himself up for her,
Eph 5:26 that he might sanctify her, having cleansed her by the washing of water with the word,
Eph 5:27 so that he might present the church to himself in splendor, without spot or wrinkle or any such thing, that she might be holy and without blemish.
Paul also applies the same principle (1 Corinthians 11:3) to the church by referring to his own culture in the rest of that chapter and in 1 Timothy 2.
1Co 11:3 But I want you to understand that the head of every man is Christ, the head of a wife is her husband, and the head of Christ is God.
1Ti 2:12 I do not permit a woman to teach or to exercise authority over a man; rather, she is to remain quiet.
1Ti 2:13 For Adam was formed first, then Eve;
1Ti 2:14 and Adam was not deceived, but the woman was deceived and became a transgressor.
You neglected to quote 1 Timothy 2:13-14 as well, since Paul grounds his "opinion" in the order of God's creation of Adam and Eve as the reason he says that women must not "exercise authority" over men, thus taking our post back where we began.
Churches who take this biblical principle seriously, as they all should, have only male pastors and elders as the leaders who set the direction of those groups.