The idea (and its practice) that women should write a different style to men was existent hundreds of years before the Spencers were selling textbooks and I think the idea is more likely to have originated with the different status and roles of men and women in American and British society leading to different expectations about how they'd use their handwriting and Spencer was simply continuing with that idea.
A book produced by George Bickham's son (also called George Bickham) in 1733 called "The Young Clerk's assistant" features two dedications : one to the young clerks of Great Britain and another to the young ladies of great Britain. The young clerks dedication states that the young men would be using their handwriting in a professional administrative capacity, whereas the young ladies dedication portrays their handwriting as a personal ornament and for writing love letters with :
Ye British Youth our ages hope & care ;
You, whome the Next may polish or impair,
Learn by the Pen those Talents to insure,
That fix ev'n Fortune & from Want Secure,
You, with a Dash, in time may drain a Mine,
And deal the Fate of Empires in a Line.
For Ease & wealth, For Honour and Delight.
Your Hand's Your Warrant, if you well can write.
Vive La Plume
Ye springing Fair whome gentle minds incline
To all that's curious innocent and fine!
With admiration in your Works are read
The various textures of the twining thread :
Then let the fingers whose unrivalled skill
Exalt the Needle, grace the Noble Quill.
An artless Scrawl the blushing Scribblers Shames
All should be fair that beauteous Woman frames
Strive to excel, with ease the pen will move
And pretty lines add charms to Infant Love
These different dedications reflect the fact that society in the 18th and 19th centuries in Britain and America was patriarchal : men usually had and were expected to have power over women (e.g coverture laws) and so men and women would (in theory at least) be doing completely different things with their handwriting. So, in order to help show this difference between men and women you would have them write different styles.
However, I believe that in the later 19th century more and more women started entering the workforcegoing into positions which were hitherto unavailable to them (esp. because their labour was cheaper than mens : Gillott mostly employed women and children to manufacture their pens) and since women might now be doing professional administrative work requiring handwriting there was no longer a need or desire for them to write a different style.
