A frequently asked question is what the term “co-Masonry” is and where it comes from. I just found the answer in Karen Kidd’s On Holy Ground.
The founder of mixed gender Freemasonry in the USA was Antoine Muzarelli who used the term “co-Masonry”. In the UK (and abroad) Annie Besant was the driving force behind early mixed gender Freemasonry. Besant called it “Joint Masonry”.
At some point the two got a discussion how this new form of Freemasonry should be called internationally, preferably not by two names. Besant set in for her term, Muzarelli objected. Two quotes from letters between the two as Kidd has them in her book.
Here [meaning: the USA] we have co-education and, on the same analogy Co-Masonry.
(page 51 of Kidd’s book).
When Besant started to push for “joint”, Muzarelli wrote:
A ‘joint house’ is, here, an immoral house; a ‘joint cave’ is a house bearing the ugly reputation of selling liquor to both sexes on the sly and without a licence. So you see, the prefix ‘joint’ is not at all used in America in the sense in which the English use it.
Muzarelli continues explaining that women would not join an order that calls itself “joint”. Besant gave in and “co-Masonry” became the internationally used term for the mixed gender Freemasonry of Le Droit Humain and close allies. I suppose later when the landscape became more splintered other groups started to use other terms to distinguish themselves.