There were and are female calligraphers of note like Yang Mei.
This calligraphic text on this fan was painted onto it by an empress of the southern song dynasty called YANG MEI.
Many cultures seem to acquire or develop the custom or restraint of women working with textiles or embroidery while men get to paint and write even when literacy and education is available.
In ancient China and other countries using writing systems based on Chinese characters even in scholarly and aristocratic families literacy tended to be limited to males. The advent of printing and books make it easier for women to acquire literacy and study calligraphy from manuals and classic texts.
With cheaper editions being available daughters and sisters could study at home and not have to wait until the boys and men were finished with precious hand copied manuscripts kept in male studies.
Beautiful and elegant as this fan is we should remember it is also an artifact of an culture in which very few women had a chance to learn calligraphy skills or the choice of whether they would prefer to learn calligraphy or embroidery.