He was a citizen of Rome. As such, he provided access the Jews would not otherwise have had, but he could not make a full divorce from strict cultural mores of the time either.

Most of the New Testament is letters from Paul to the various churches he established, which is why it appears so contradictory. They each had different questions and different needs.

There are other passages where he exalts women. Thecla traveled with Paul, became a healer, escaped death via miraculous intervention many times, and was martyred. Phoebe was recommended as a deacon to the church at Cenchreae so she was a minister. Prysca, Nymphs, Lydia, Mary were listed as leaders of house churches. Mary, Tryphanea, Tryphosa, and Persis were said to have “worked hard for the Lord". Junia and Andronicus were in prison with Paul and he refers to them as Apostles.

Romans of the time refered to early Christianity as the religion of women, children, and slaves.

It seems clear that Christianity thrived and grew throughout Rome through the teachings, support, and work of women as much (maybe even more) as men. Modern efforts to exclude women only erode the message and life of Christ by seeking to re-establish and reinforce patriarchy.

Read the Gospel again. Jesus was clearly opposed to patriarchy, particularly spiritual patriarchy. No one needs an intermediary between them and the divine. No one needs permission from another to teach, heal, or prophesy if God calls you to do it.

Jesus admonished us time and time again to turn our sight away from trappings of the world, including cultural mores, and set our sights on the divine and heaven. Anything, anything that works against that principle of universal agape love should be further examined with the closest scrutiny and challenged openly because that thinking did not come from Christ.