Why was there never a female Shakespeare?

Virginia Woolf, whose influence hangs over many female lives, argued that privacy and economic independence are necessary for a woman to write at all. If she wanted to write as she pleased she must also be able to move freely in the world.

And addressing the question of why there has been no female Shakespeare, Woolf traces the likely career of her imaginary and equally talented sister Judith, following her from patchy education to rebellion and flight to London, where every door including the stage door is closed to her and the streets are dangerous.

There follow with Judith Shakespeare,  a pragmatic liaison, unwanted pregnancy, suicide and an unmarked grave at ‘some crossroads' where the buses now stop outside the Elephant and Castle.