Here's the thing. I brought up my Greek prof because he is a renowned world authority on translating Greek, including exegetical issues. His father, Robert Mounce is a renowned Greek scholar, his cousin, Daniel Wallace, is the top Greek grammarian in the world.
I told you to read his extensive Word Commentary on this passage after 40 some pages, Bill Mounce comes to the same conclusion as this not so famous old lady writing this. (And not so experienced!) The passage ultimately DOES rest on the single word, authentein, and how it is translated. Mounce himself said that to me in class. The word authentein is a tangled problem, because of being a hapax legomena! How you choose to translate the word depends more in your personal feelings toward the relationship between men and women. Are men special, and the only ones able to serve God in ministry? You simply have failed to prove it scriptural. Your exegesis is wrong!
Complimentarians harp on the roles God gave to Adam and Eve after the Fall in the Garden of Eden. Christ is the second Adam (Romans 5) and he has freed us from the Fall, and the ugly roles that were placed upon both men and women as a result of the Fall. Why would anyone not celebrate that Christ has set us free from sin, which includes sin in the Garden which we all bear, and the end of roles as part of the law. Jesus destroyed roles on the cross, by defeating Satan on the cross.
Why not live in the light of eternity, since Christ has born our place in the cross, and we are being set free from sin and death? We are being sanctified now, by the power of the Holy Spirit. Soon, we will see Jesus face to face, and we will be like him, for we shall see him as he is.
As for didaskein, it is a term used by rabbinical students. They were not to teach, until they were judged by their master to fully understand the truth of God's Word. Women, mostly illiterate, need to sit quietly and learn, first how to read, and then the gospel. Then the deeper things of God.
Instead of being second class, as in the Roman, Greek and Jewish societies, women were given the right to be saved, follow Christ and to study to show themselves workers approved. Jesus set women free from their bondage, when he died. That sin started in the Garden, but women and men were redeemed and changed by the power of God. If you want to park on Genesis 3 and the results of roles as a consequence of sin, go for it! I am living as a set free New Testament Christian, free to worship God, to learn and grow in my faith, as an equal to any man.
As for Gal 3, you have fallen into the same foolish trap Paul warns of in the beginning of the chapter. You are trying to live by the law, not the Spirit!
"You foolish Galatians! Who has bewitched you? Before your very eyes Jesus Christ was clearly portrayed as crucified. 2 I would like to learn just one thing from you: Did you receive the Spirit by the works of the law, or by believing what you heard? 3 Are you so foolish? After beginning by means of the Spirit, are you now trying to finish by means of the flesh? 4 Have you experienced so much in vain—if it really was in vain? 5 So again I ask, does God give you his Spirit and work miracles among you by the works of the law, or by your believing what you heard? 6 So also Abraham “believed God, and it was credited to him as righteousness." Gal 3:1-6
Mid-chapter, Paul discusses the Seed which is Christ. And how we are one in him. Not first and second that is found no where in scripture. It is a lie from Satan to divide men and women from each other and Christ.
Your hermeneutics supports the division Satan created between God and humans, and man and woman. You are trying to keep alive the consequences of sin, not the result of Christ's death in the cross!
"Whom the Son sets free us free indeed!" John 8:36
Christ came to reconcile us to God and one another. look what Paul states later on in Galatians 3. Christ is the seed of Abraham and we do not claim our inheritance because of the law, but by grace.
"15 Brothers and sisters, let me take an example from everyday life. Just as no one can set aside or add to a human covenant that has been duly established, so it is in this case. 16 The promises were spoken to Abraham and to his seed. Scripture does not say “and to seeds,” meaning many people, but “and to your seed,” meaning one person, who is Christ. 17 What I mean is this: The law, introduced 430 years later, does not set aside the covenant previously established by God and thus do away with the promise. 18 For if the inheritance depends on the law, then it no longer depends on the promise; but God in his grace gave it to Abraham through a promise.
19 Why, then, was the law given at all? It was added because of transgressions until the Seed to whom the promise referred had come. The law was given through angels and entrusted to a mediator. 20 A mediator, however, implies more than one party; but God is one." Gal 3:5-10.
The promised Seed is Christ Jesus. We are joint heirs in soteriology, but we can also claim to be heirs and equal with men, as Paul finishes the chapter, below!
(Your exegesis brings not only faulty, but learned from i Er zealous men!)
"So in Christ Jesus you are all children of God through faith, 27 for all of you who were baptized into Christ have clothed yourselves with Christ. 28 There is neither Jew nor Gentile, neither slave nor free, nor is there male and female, for you are all one in Christ Jesus. 29 If you belong to Christ, then you are Abraham’s seed, and heirs according to the promise." Gal 3:26-29
I belong to Christ! I am Abraham's spiritual seed, the same as any man or woman who has given their life to Christ and follow him. I am free to follow the calling of God for my life. I am a pastor, I feed my sheep in my ministry. God called me once to go to seminary, and I did not go. My stumbling block was that only men are pastors. My life went downhill, so when God called me 15 years later to go to seminary, I answered the call and God trained me and gave me the most amazing ministry working with the hurting and broken. Praise God!