Whether or not one agrees with the interpretation, there is a reasonable biblical case to be made that a woman should not preach or teach in the church.  Paul writes in 1 Tim 2:

>8 I desire then that in every place the men should pray, lifting holy hands without anger or quarreling; 9 likewise also that women should adorn themselves in respectable apparel, with modesty and self-control, not with braided hair and gold or pearls or costly attire, 10 but with what is proper for women who profess godliness—with good works. 11 Let a woman learn quietly with all submissiveness. **12 I do not permit a woman to teach or to exercise authority over a man; rather, she is to remain quiet.** 13 For Adam was formed first, then Eve; 14 and Adam was not deceived, but the woman was deceived and became a transgressor. 15 Yet she will be saved through childbearing—if they continue in faith and love and holiness, with self-control.

A theological justification for the point then is this - Eve was deceived, and therefore all women can no longer be trusted. It is, in fact, Scriptural, using a very plain sense reading of the text.

That said, there are varying interpretations and contra-indications to such a plain instruction.  (2 John being addressed to "the elect lady and her church" comes to mind.)  But, if the standard interpretation is the *sensus plenior* here, then the Bishop of Rome would simply being saying that the church has no authority to create a new teaching out of a very old Scripture.