The headcovering passage and others reveal that women were considered teachers and prophets in the congregations under Paul. The headcovering bit is hard to be certain about but may have arisen due to a extant belief that women's hair was a sexual organ of sorts. Perhaps this explains the reference to angels, that is to avoid tempting angels when women had contact with them during prophecy or inspiration. Also certain Mystery cults of the day directed the women to have their heads covered in the ceremony until the conclusion when all were declared equal and the hats removed. Perhaps the covering itself was drawn from this tradition like so many other aspects of Pauline Christianity, then again perhaps his insistance that women keep the hat on was to differentiate the cults and placate the men who had a problem with this notion of equality.
! Cor 14:34,35 is regarded as a postPauline interpolation (addition). This is so for a number of reasons, the most obvious is that if removed from the text it reads unbroken. Even some manuscripts have these words located elsewhere, betraying that the words were addtions yet to find a permanent home.