The entire prohibition against women teaching is sourced in a few sentances in Paul's letters and routinely taken out of the context of his humanity and his good ministry. As to the first point, Paul was Paul, a human, sinful and as lost as any of us. He was not the Christ, and he himself repeatedly affirms that he is not to be treated as the Christ. Paul himself describes that in Christ there is no male or female, that love trumps everything, that love is NOT insistance on one's own way, that placing a law of any kind above the work of the Holy Spirit destroys the power of the Gospel. He repeatedly confronts believers to get out from being under religious law (like circumcision), but then he ardently applies religious law to women regarding silence and head covering. And there's the rub... But seriously, who can blame him, those days were very oppressive towards women - that was the norm - he was officiating in his present time. Paul was a single man, who was doing his absolute best to share the Gospel and keep his congregations from falling into chaos. He just displayed his humanity from time to time, blinded by his own blind spots, passing judgement that can't be passed, etc...just like us. It's not like he was Jesus, after all.
So anyway, the vast weight of history through scripture supports that women are not prohibited from leadership by God, though it obviously seems strikingly less frequent. I don't want to get too deep into the historical aspect, but it is worth mentioning we are in the very first era in human history - really only about 30 years of the entire human history - in which women have been granted any semblance of equality or opportunity, and that is only happening here in Western society. It is only here and now that men and women may each individually grapple with serving God with their entire mind, body and spirit to their best capacity. It is only here and now that each person can truly be treated as a creation who God has ordained for good work in such a time as this. That is an exciting opportunity for the body of Christ.