It's based primarily on Paul's words in 1 Timothy 2:12, where he states he does not allow a woman to teach or to take a man's authority (which is the actual meaning of the Greek; it is not to take authority 'over' a man...).
One of the things that has interested me is that there is no mention of what a woman is not to teach, even in the context. The clue is actually in the Greek, as I mentioned in an earlier post. The verb used which translates 'teach' indicates the authority of a formal instructor over a student even to the point of corporal punishment. It is the word from which we get 'didactic.'
If to 'teach' actually means simply the sharing of information, whether biblical or secular (and the distinction is not made in Paul's letter there), then Baptist Board is in violation of Scripture for allowing women in a forum on theology, for instance. Someone might actually 'learn' from something one of us says!
That is obviously, I think, not what Paul is talking about. He is, instead, referring to a woman assuming a man's authority in any area, including teaching 'under her own authority' in ANY circumstance. For, as Paul explains, it was woman who was deceived, not man.
And I understand that and know that, as a woman, I truly can be easily deceived. My kids found that out quite early! Sincerity gets me just about every time! And so my teaching, even in school, was subject to both principal and parents. And when I am with my husband and we are presenting, I am totally accountable to him for what I say and present. I'm quite comfortable with that, and find it in no way to give me permission to give sermons or otherwise lead in a church -- simply to stand alongside him as his partner and present with him. This saves him some stress, actually, and he prefers it when I present in the areas I am more familiar with, such as biology and linguistics.
However, there are those, such as our friends from this weekend, who feel -- and quite strongly -- that a woman should never teach anything to do with the Bible to a mixed group, whether her husband is there or not. The more Barry and I have studied what Paul was saying and how the Bible interprets Bible, the more we feel they were definitely off on the wrong track.
Should something happen to Barry, I am the one most familiar with a lot of his work, and I can guarantee here and now that I would do my best to keep that work going so that people could learn from what my incredible husband has accomplished.