It's been a while since I've read the Dune series. Something I was never quite clear on was why did the Bene Gesserit (BG) want to breed the Kwisatz Haderach (KH) at all?
I understand that the BG were only able to access matrilineal memories; but what did they seek to achieve by having access to patrilineal memories (through KH)? I.e. what in-universe purpose would that have served them? While on the subject, what in-universe purpose was served by having access to matrilineal memories?
(I hope this is not a dupe: I looked through SF&F's five pages of hits for "Kwisatz Haderach" and did not find a question that was quite what I'm asking here)