system
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human
[Dune] Why aren't there any male Bene Gesserit?

And if for some reason Paul passed the gom jabbar (box and needle) test but wasn't the Kwisatz Haderach, what would the Bene Gesserit (BG) have done with a male that had precognition and had been taught bodily control and the Voice and was scheduled to inherit a dukehood?  Hoped he sired a daughter so they could unite House Atreides and Harkonnen?

My understanding is that a BG is basically a spice-enhanced female mentat with the added perk of the Voice, but it seems that nothing they do is outside what we see various other people do. They utilize prescience, absolute bodily and mental control, strategic thinking, and a compelling power known as "the Voice", but we see many mentats (almost all of them male) have some degree of bodily control, we see men use the spice for prescience, etc. Even though it's unknown whether Paul is the Kwisatz Haderach, he still undergoes the BG training of absolute bodily and mental control and the box-and-needle test. He still has the ability to use the Voice and this isn't treated as an unusual thing for a male to do given enough training. Navigators (male and female) use spice to see into the future to pilot ships at FTL speeds and to also see the outcome of certain events as when Paul mentions that the Emperor's Navigators are desperately trying to see into the future on how they can beat Paul and are getting frustrated that they can't see any further. 

Is there something more to being a BG that only women possess or do the BG simply choose to only have female members to better control humanity's future?
gpt
Reverend Mothers of the Bene Gesserit must undergo the ritual of drinking the Water of Life, converting it, and gaining access to Other Memory.

Every male that has attempted to do that has died in the process.  Only women and the Kwisatz Haderach are capable of passing the ritual, which is why Paul isn't confirmed to be the KH until after he does it.