Women should be silent in the churches. for they are not permitted to speak, but should be subordinate, as the law also says. If there is anything they desire to know, let them ask their husbands at home. for it is shameful for a woman to speak in church. (1 Cor 14:34-35)
According to a study now available at Evangelical Textual Criticism, Paul did not write those words. They were added some time later by a different hand.
The theory that these words are a scribal interpolation into the Pauline text is one of four possible interpretations of these verses. The second is that these words are genuinely from Paul, but they are a quotation of of his opponents (since when does Paul appeal to what “the law also says”?). Beginning verse 36, “Or did the word of God originate with you?” Paul challenges this argument. (That first Greek particle can also be translated as an expression of surprise introducing Paul’s counter argument. The Amplified Bible actually takes this approach and translates [paraphrasing from memory], “What? did the word of God originate with you?”)
A third possibility is that these are Paul’s words, but they are written with reference not to women preaching or speaking at all, but with unruly speech—such as might have been expected in a cultural milieu where half of the congregation (the men) had been socialized about acceptable behavior in the city assembly or listening to a teacher at the gymnasium but the other half (the women) had previously been banned from these venues. Thus, in order to participate in Christian worship, the women now needed a “crash course” in the proper etiquette for a public speech or debate.
Finally, it could be that Paul intended by these words to forbid any sound coming out of any woman’s mouth at any time during Christian worship. How a woman is supposed to “pray” or “prophesy” in the Christian assembly under those restrictions (1 Cor 11:5, 13) is a mystery to me.