1. Patriarchy- keeping women oppressed so they can't compete with men,
2. Tribalism- keeping the bloodlines pure. In ancient times, allowing enemies around females was an invitation to rape and pillage; women ended up pregnant and bore the offspring of invaders.
Now, of course, no woman has to remain pregnant if she doesn't want to, and we've kind of moved beyond the idea that foreign blood is contaminated, anyway, or that bearing the offspring of people who are different from us weakens us as a nation or a people.
Even in ancient times, people just dealt with this minor inconvenience.
Jews decided that Jewishness is passed through the maternal line. In many African tribes, nobility passed to the chief's sister's male offspring, rather than to the male offspring of the chief himself. Only by passing leadership on to his nephew could the purity and continuity of the royal bloodline be 100% assured.
All over Europe, we see the genetic results of ancient plunder; this 'foreign' blood hasn't weakened the European people, it's strengthened them. The Black Irish- who likely have some Iberian blood- can withstand the sun without dying of melanoma, while those of unadulterated celtic blood are unlikely to live to old age without treatment for malignant skin lesions.
Regardless, we should be beyond that sort of thinking today.
Unlike some woman from a millenium ago (or a Southern Belle from two centuries ago, or a fundamentalist Islamic woman shrouded in hijaab today), I am not willing to cower in some dark closet and miss participating in the larger world, just because rape- and even impregnation by rape- is a possibility.
That would be a foolish waste of a life, and we only get one.
If all women behaved thus, it would be a ridiculous waste of strength and resources as well; we would not have won WWII without the aid and participation of females.
We will not, as a nation, accomplish future goals, without women working side by side with men as equal partners.