I'm sure i read thru some posts a day or 2 ago, but here, i'm posting some verses that came to mind (not sure anyone else has posted them):
Titus 2. 3 The aged women likewise, that they be in behaviour as becometh holiness, not false accusers, not given to much wine, teachers of good things;
4 That they may teach the young women to be sober, to love their husbands, to love their children,
5 To be discreet, chaste, keepers at home, good, obedient to their own husbands, that the word of God be not blasphemed.
While there's no clear instruction to separate the men and women here, the older women are instructed to teach the younger, and what better way when they are together, perhaps in smaller groups in fact or one in one.
In conferences or women's prayer gatherings, some pastors or workers are also invited here, and i didnt think it was exclusive, but topics are often geared to women's needs like inner beauty, etc. which men may not always need or be interested in=).
Our church prayer mtg start with men and women together reviewing previous sunday's msg and individual shares of praise and trials, then divide among men and women perhaps for more personal prayer items not to be broadcast to all. But small care groups are often separately done. I think it is for privacy and more personal needs of both groups to be able to share and unload unashamed, unlike if when the group is mixed. As there are other church fellowships like interchurch events, there are a few opportunities to mix with men.
I also understand the advantage of mtg with a smaller group of your own gender, for one, because maturity of believers is so varied. I'd have appreciated 'family' Bible studies w/ all ages, children to grandparents together... but just getting them together may not be easy unless it was a family's reunion and all ages are indeed present! But a Bible study at the house of a bro or sis does not mean other members of the household cannot join.