My personal conviction is that Paul is quoting/refuting a mistaken position. The language, tone, style, textual context, historical context, and known facts about Corinth and Paul's praxis indicates this to me.
This is essentially the same position taken by Fitzmyer:
"Verses 34–35 are considered to be a quotation of what some Corinthian Christian men have been maintaining against women who have been speaking out in cultic assemblies. It has come to Paul’s attention, just as did the slogans quoted earlier in the letter (6:12, 13; 8:1, 4, 5; 10:23). Paul’s reaction to the statement quoted is expressed in v. 36, which is introduced by the disjunctive particle ē, “or,†used here twice with two rhetorical questions (as also in 11:22b), along with the masc. monous modifying hymas, referring to such Corinthian men. So (with differing nuances) Bilezikian, Flanagan, Gourgues, Kaiser, Snyder, Odell-Scott, Talbert. ... In this case, the three verses were written by Paul, but vv. 34–35 are the quotation of a view that is not his. His reaction is expressed in v. 36, vague though it is, and its implication would be egalitarian and would contradict neither 11:5 nor Gal 3:28. Even though this last interpretation may not fully satisfy either the understanding of v. 36 or its connection with what precedes, it is better than the other interpretations, pace Hays (1 Cor, 248), Garland (1 Cor, 667); and it rightly severs the close connection of v. 36 to vv. 34–35, as even Murphy-O’Connor (“Interpolations,†90, 92) has recognized.... Women should remain silent in the churches. Lit. “let women be silent in the cultic assemblies,†i.e., in the various house-churches of Corinth. Paul quotes the saying of some Corinthian men who undoubtedly might allow the women to join audibly in “Amen†to a prayer, as in the thanksgiving of 14:16, but would exclude them from any form of active public speaking in churches (now in the plur., in contrast to the sing. “church†used so far in this chapter [vv. 4–5, 12, 19, 23, 28]); the prep. phrase echoes 11:16c. Some MSS (D, F, G, K, L) add hymōn, “your (wives),†which is otherwise omitted in the best MSS. In either case, one should note the difference from 11:5, where the sing. gynē is found, whereas here it is plur. hai gynaikes. The silence is general and absolute, and not merely while someone else is speaking (v. 30), as Kremer (1 Cor, 312) would have it; nor does it refer to something specific (like idle gossip).... What, did the word of God originate with you? Lit. “Or, has … come forth from you?†This verse, with its double-rhetorical question, formulates Paul’s reaction to the attitude of Corinthian Christian men quoted in the two preceding verses. Paul’s phrase, ho logos tou theou, may be derived from LXX Jer 1:2, but he is using it in the sense of the “gospel,†the Christian message, as in 1 Thess 2:13; 2 Cor 2:17; 4:2; Rom 9:6. In the LXX the more common phrase is logos kyriou, “the word of the Lord,†a communication from Yahweh. Paul wants the Corinthian Christian men to realize that neither the gospel nor its implications for life have had a starting-point among them, and so they are in no way a law unto themselves. This interpretation of v. 36 seeks to give full force to the introductory ptc. ē, “or,†which Paul often writes when introducing rhetorical questions (e.g., 1:13; 6:2, 9, 19; 9:6; 11:22). Along with the RSV, I have translated it as “What!†in the lemma above. It marks an alternative, as it introduces the two questions that express Paul’s impatience with the attitude of such Corinthian men expressed in vv. 34–35." [Fitzmyer, J. A. (2008). Vol. 32: First Corinthians: A New Translation with Introduction and Commentary. Anchor Yale Bible (533). New Haven; London: Yale University Press.]
