Why did men only play in Shakespeares plays?

Answer 1

Because back then only boys could do anything. The girls sat at home doing chores.

(Actually, women were allowed to work. Required to for poorer women, even. Acting was just seen as scandalous and immoral, barely acceptable for a man, way too demeaning for a woman.)

Answer 2

It was a social prohibition. It is thought that the life of an actor was beneath the dignity of women, or was too unseemly for women to be seen in public in such an undignified undertaking.