1 Tim. 2:8 I desire, then, that in every place the men should pray, lifting up holy hands without anger or argument;
That is that men should raise their hands in prayer in every church within the context of the liturgy. Today, in Orthodox, Catholic, and many Anglican services, it is the priest who raises high the eucharistic cup. This is what is being referred to. Men should lift their hands high as they adore the eucharistic cup, not women. Excluding the priesthood to women.
2:9 also that the women should dress themselves modestly and decently in suitable clothing, not with their hair braided, or with gold, pearls, or expensive clothes,
Women should dress themselves modestly in church. They are not coming to show off their fine jewelry or their hair. In another text, Paul asserts women should cover their hair (1 Cor. 11:10)
2:10 but with good works, as is proper for women who profess reverence for God.
All should be adorned with good works. Not just women. But women especially who profess reverence for God should.
2:11 Let a woman[wife] learn in silence with full submission.
The liturgy should be a quiet place so as not to distract anyone, including a wife, to learn in submission.
2:12 I permit no woman[wife] to teach or to have authority over a man;[husband] she is to keep silent.
Within the liturgy, a wife is not supposed to hold authority over her husband and must keep her questions silent until after the liturgy.
2:13 For Adam was formed first, then Eve;
This uses an established order of creation to defend this position.
2:14 and Adam was not deceived, but the woman was deceived and became a transgressor.
Marital establishment–it was Adam’s wife who was deceived.
2:15 Yet she will be saved through childbearing, provided they continue in faith and love and holiness, with modesty.
That is, the will to bear children if either the woman or her husband is unable to reproduce. Marriage is established for the purpose of participating in God’s act of creation. A marriage where the wife and husband willingly choose not to bear children is a mortal sin.