So the Bible Apostle Paul says "I do not permit a woman to teach".
As a matter of fact, this seems a little strange. In 1 Cor 11, Paul talks about how the congregation should organise their activities, and in verses 4-5 he suggests how men should expose and women should cover their heads whenever he/she "prays or prophesies", typical activities in a congregation. (To prophesy means not only to predict, but also to talk with divine inspiration). It would seem unreasonable that on one hand, Paul should tell how a woman should dress while speaking with inspiration in the congregation, and on the other hand that she should not speak in the congregation. Especially considering Gal 3:28: "there is neither male nor female".
In his book Misquoting Jesus, Bart Ehrman mentions the prominent role of women in the early Christian congregations, and how this has been concealed by minor changes in later manuscripts, e.g. Acts 17:4, where the original wording probably talked about "some of the principal women", although newer manuscripts say "the wives of some of the principal men". (In fact, this is a verse where the NWT actually agrees with many other Bibles in using the "principal women" wording.)
Ehrman also mentions 1 Cor 14:34-35 about women being expected to be silent in the congregation and be taught by their husbands. Not only is it strange for this admonition to appear in a letter where Paul has just told the women how to dress when they speak in the congregation. It is also strange to place this admonition inside a sequence that is actually about the role of prophets in the congregation, it looks like an unmotivated sidetrack. If we remove the two verses and go right from verse 33 to verse 36, then the text flows better. And surprise, the two verses about silent women are absent from some old manuscripts, and in others they are found at a different place (after verse 40). It simply looks like these two verses have been inserted at a later stage by someone who was not Paul. The two verses are rather similar to 1 Tim 2:11-12, and the verses in 1 Cor may originate from a marginal note in an old manuscript, referring to 1 Tim. But according to Ehrman, most scholars today would agree that 1 Tim was not written by Paul.
Ehrman's account is more detailed and has more evidence than I have presented here. The book is relatively neutral to theological discussions, but I'd recommend it because it explains the science of textual criticism in a way that laymen can understand. Of course, fundamentalists don't like books like this one. Even though they base their Bible interpretations on Bible versions that have been edited on the basis of the exact same principles that Ehrman tells us about. :)