Eh. They’re giving you a simple explanation that’s not rooted in core church doctrine, so much as a later offshoot of it. The biggest impediments are passages in scripture such as:
Women should remain silent in the churches. They are not allowed to speak, but must be in submission, as the law says. If they want to inquire about something, they should ask their own husbands at home; for it is disgraceful for a woman to speak in the church. 1 Corinthians 14:34-35 NIV
and
A woman should learn in quietness and full submission. I do not permit a woman to teach or to assume authority over a man; she must be quiet. For Adam was formed first, then Eve. And Adam was not the one deceived; it was the woman who was deceived and became a sinner. But women will be saved through childbearing—if they continue in faith, love and holiness with propriety. 1 Timothy 2:11-15 NIV
These two passages are the words of the apostle Paul in his first letter to the church in Corinth and in his first letter to his student, the apostle Timothy. Next to Jesus himself, no one figure has had as much influence on Christianity and its practice as the apostle Paul, considered a Saint by nearly all Christians. For those that believe that the Bible is the literal and inerrant word of God, the words in the two passages quoted above become more than just St Paul’s opinion however, they become God’s will.
I’ll note that nothing is recorded of Jesus himself ever speaking on this subject. Jesus was highly protective of women, and he also intervened in support of one of his female disciple’s right to learn along with his male disciples when Jesus was asked to send her back to the kitchen. And if you read Jesus’s words alone, you get the sense that Jesus had an issue with the way men of his time (mis)treated women. Nevertheless the lack of any recorded teaching by Jesus on the subject of women leading or teaching men gave St Paul room to weigh in and set the church’s doctrine himself and that binds more traditional churches to this day.
Yep, the qualifications for deaconship are established in 1 Timothy 3:8-12 and there is a bit of linguistic wiggle room to conclude that when St Paul speaks of women, he is referring to female deacons, aka deaconesses instead of the wives of deacons as most believe. Regardless, given his words only one chapter earlier, it’s fairly clear he doesn’t want them teaching or leading men either way. So administrative functions and teaching children and other women may well be ok as far as St Paul is concerned, but preaching in the pulpit to adult men or leading the church as a whole, both priestly functions, are not.