If we must!

As I recall the Deir el Medina ostraca indicate a high level of literacy -
including women - in that community. Which was of course in no way typical.
The Hekanakte letters, from an earlier period also show a good deal of letter
writing going on in a large priestly household.

Women don't seem to have enjoyed - if that's the word - formal education
but given that some were undoubtedly literate I suspect that some 'white
kilt' class families saw fit to educate their daughters privately. And I
suspect any girl in a literate family could persuade somebody to teach her
if she was really interested.