> So for #1 and #2, you just hand-wave your doctrine as "miracles" that defy all otherwise known and consistent laws of the universe. Doesn't seem like intellectual integrity to me.

It is not intellectually dishonest to believe that God, who governs the universe and it's laws is able to suspend them if he so chooses.

> Why don't you admit that the reason the Catholic church does not allow women priests is not because "a women's function is laborious" (a function not all women naturally can even do, otherwise why can't barren women be priests?), but rather because you take the words of Paul literally and do not allow a woman to hold authority over a man? That's the real reason and you know it.

No, that is not the real reason. The idea that men and women are complementary is rooted in Christian teaching since the beginning. My understanding is that the reason women are not allowed to be priests is partly because during mass the priest stands in for Christ ( in persona Christi ) and Christ was born a man. Women hold authority over men all the time in the Catholic church, many doctors of the Church are women.

> Also, the "faith alone" thing is a bit misunderstood to be honest, mostly caused by how protestants overload that word. They basically mean that you cannot be saved by works alone under any circumstance, and that if you are unable to produce any works but have faith, you can still be saved (the example here is the penitent thief on the cross). After that, they consider works to be a natural outcome of legitimate faith, and that if you have the chance to do works and don't you'll lose your justification by faith.

This is just a long winded way of saying you are not saved by faith alone.

Doctor of the Church means a teacher whose teachings are universally applicable to everyone in the Catholic Church. It has nothing to do with authority. Many nuns were traditionally teachers of children, too. And each of the female doctors of the church, as far as I know, where nuns who submitted all their teachings to their superiors and confessors, who then examined and verified her writings for orthodoxy (1 Timothy 2:14) before recommending them for others or permitting them to be published (cf. Imprimi Potest).

St. Paul's words come from a deeper natural distinction between man and woman, and have to do with the fall of Adam and Eve, where Eve was the one who was deceived by the serpent, and also that Eve was created from Adam, and thus woman from man. Man was created first, because man is the default gender of humanity, and from man came woman. "But now man is born of woman," St. Paul also says, "and all things are from God." We are equal in dignity but not in our roles. Some women cannot bare children, but all men cannot bare children. Some men cannot be priests, for example if castrated, yet all women cannot be priests, because man is the gender God assigned to fatherhood and leadership, to represent his fatherhood and paternal leadership. Yet we are not to lead as the world leads, by "lording it over" others; we are to lead as Jesus led, meekly, humbly, with gentleness, by example, and doing everything in our power to help those whom God has put in our charge to accomplish their duties, unlike the Pharisees who "lay heavy burdens" on their charges "but will not lift one finger to help them carry it." Everyone has the heavy burden of going through a wearisome life, and our jobs as fathers are to show them how to make that burden lighter, first and foremost by bringing them to Jesus, who says "Come to me, all who labor and are heavy laden, and I will give you rest. Take my yoke upon you, and learn from me; for I am gentle and lowly in heart, and you will find rest for your souls. For my yoke is easy, and my burden is light."

St. John Paul II talked a lot about this subject about 45 years ago, here's a PDF with a clickable table of contents: https://d2wldr9tsuuj1b.cloudfront.net/2232/documents/2016/9/...