After 1650 the female roles were played by women. Before that, and rarely since, boys played the women's parts. More recently it is common to find women playing the men's parts (Shakespeare wrote more parts for men than for women mainly due to the shortage of competent boy actors).
It wasn't so much that females were discriminated against or thought not as important. Women were not allowed to act because it was considered to be indecent for a woman to show herself before a group of men. After 1650, women appeared on stage, but they were still thought of as indecent women.
Males
I don't know what Elizabeth you are speaking of, but I presume it was because she was a female Shakespearean actress who was acting after the year 1660 sometime. Sometimes actresses play the male roles in Shakespeare as well.
Females were not allowed to play on stage so men and boys played all the female roles.
Shakespeare is not the only dramatist of his time to write plays with leading female roles. John Webster's plays The White Devil and The Duchess of Malfi also have strong female leads. The reason probably has to do with the quality of performers in the company. Shakespeare wrote specifically for the actors in his company, and clearly there were a number of talented boys for whom Shakespeare felt confident writing roles like Rosalind, Viola, Isabella and Helena.
Women did not participate in Shakespearean plays. All roles, including female ones, were played by men.
The female roles in Shakespeare's day were performed by Boy Players: young actors who had not yet reached puberty and therefore did not have masculine voices. Some of the Boy Players were Apprentice Actors, the modern equivalent would be Interns.
Males
In Shakespeare's time, all female roles were played by young boys or men because women were not allowed to perform on stage. This was a common practice due to societal norms and restrictions at the time.
Young boys played the role of women.
Young boys played female parts. It was against the law for women to act.
my mum
I don't know what Elizabeth you are speaking of, but I presume it was because she was a female Shakespearean actress who was acting after the year 1660 sometime. Sometimes actresses play the male roles in Shakespeare as well.
Females were not allowed to play on stage so men and boys played all the female roles.
Most of the time, all roles were played by men.
Males played both female and male parts, because acting was not a "suitable" profession for women at the time.
Shakespeare is not the only dramatist of his time to write plays with leading female roles. John Webster's plays The White Devil and The Duchess of Malfi also have strong female leads. The reason probably has to do with the quality of performers in the company. Shakespeare wrote specifically for the actors in his company, and clearly there were a number of talented boys for whom Shakespeare felt confident writing roles like Rosalind, Viola, Isabella and Helena.
Women were barred from the stage. Female parts were acted by Boy Players whose voices had not deepened through puberty. Some were apprentices learning the art of acting as a profession. On occasion older men might play comic women characters in the same way that Monty Python or Tyler Perry do women's roles.