Why would it have been impossible for a woman to write Shakespeare's plays according to Virginia Woolf in "A Room of One's Own"?

In this section of her brilliant essay, Woolf shows why it
would have been impossible for a woman to write Shakespeare's works by imagining that
Shakespeare had a very talented sister called Judith. By creating this imaginary sister
and comparing the kind of life and opportunities that both she and William would have
had, Woolf presents a compelling case at how women were and are impoverished by society.
Note some of her arguments:

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But she was not sent to school. She had no
chance of learning grammar and logic, let alone of reading Horace and Virgil. She picked
up a book now and then, one of her brother's perhaps, and read a few pages. But then her
parents came in and told her to mend the stockings or mind the stew and not moon about
with books and
papers.

Although she would
have "scribbled" occasionally, she had to hide her writings in case her parents burned
them. Then she is forced or blackmailed emotionally into marrying someone who is not her
intellectual equal. Even when she flees this situation to pursue her dream of acting,
she is not given any opportunity to do so, and is seduced and, finding herself pregnant,
kills herself and dies frustrated and unsatisfied. Throughout this section of the essay,
the emphasis is on the lack of opportunities that women have compared to men in every
sense of the word.