The explanation offered by some scholars, which most resonates with me, is that these verses were a marginal addition, not original to the original writing by Paul. But the fact that they are included in all manuscripts indicates that they were added very, very early, and I believe, likely by Paul himself. If you've ever written a hand-written letter, and finished it, and then realized you needed to add one more little thing, you understand that a letter writer might add that last little thing in the margin next to the topic where it belongs. The scribe who made the parent copy of the Western manuscripts may not have been able to tell where Paul intended the text to be inserted, so merely added it to the end of the section, after verse 40.
In addition to this theory, there is another possibility about this text which I would urge you to consider. Much of 1 Cor was written in answer to issues about which the Corinthians had written to him (1 Cor 7:1). As he deals with these issues, one by one, he often quotes something the Corinthians have said, and then responds to that quote, such as:
- "It's good to not have sex", but to avoid temptation, get married and have sex (1 Cor 7:1ff), or
- "We have knowledge", but knowledge puffs up whereas love builds up (1 Cor 8:1), or
- "All things are lawful", but not everything is beneficial (1 Cor 10:23).
In this marginal addition of 1 Cor 14:34-35, perhaps Paul is remembering, after finishing his letter, one more thing he needed to address. So he quotes what some factions in Corinth (1 Cor 1:10) are saying, that "Women should be silent, just as the law says."
It seems odd that Paul would be the one saying this; after all, he's already approved of women praying and prophesying in the assembly back in chapter 11. He also quotes the Old Testament when he makes a point from the law, but there is no quotation provided here. Furthermore, there IS NO Old Testament law that says women are to be silent. Why would Paul lie about what the law says?
This view makes sense of the text. Paul has just written three entire chapters about how people who are gifted by God should use that gift to build up the community, and that even if that gift comes in the form of something as impractical as speaking in a tongue, it should not be forbidden from being exercised for the good of the community (1 Cor 14:39). His whole point is that God gives EVERYONE a gift to be used for the building up of the church (1 Cor 12:7). Now he has a faction in the Corinthian church telling women that they should squelch the gift that God has given them? And what is Paul's response? He says...
"What?! Has the word of God come to you [men] only?! Are you the only ones it has reached?" (I believe the bracketed "men" is justified, as the gender within the Greek shifts to a masculine form, even though the previous prohibition was directed at the feminine group.)
If this view is correct, we've entirely misunderstood 180 degrees what this text has said, for over 2000 years.
So I ask a question: If all you know of Jesus and his church came from the life accounts of Jesus (Matthew, Mark, Luke, and John), would you conclude Jesus to be in favor of hushing women from using his gifts to spread his word? In other words, what would Jesus do? Would he tell women to sit down and shut up, or would he encourage them to use their God-given gifts to build up his community of believers? Then compare your conclusion on that matter with the possibility that Paul wasn't telling women to shut up, but was scolding those who were.