How does Shakespeare bring out the idea of feminism in his play Othello?
As feminism was not invented until the twentieth century, William Shakespeare, in the sixteenth century, could not have been acquainted with it. While it is possible to create a feminist critique of Shakespeare's works by applying 20th century ideas of feminism to them, that is different from attributing feminist intentionality to Shakespeare himself, and runs the risk of anachronism.
Feminist approaches to Othello usually focus on the character Desdemona who describes her own role as follows:
DESDEMONA: "My noble father,
I do perceive here a divided duty:
To you I am bound for life and education;
My life and education both do learn me
How to respect you; you are the lord of duty;
I am hitherto your daughter: but here's my husband,
And so much duty as my mother show'd
To you, preferring you before her father,
So much I challenge that I may profess
Due to the Moor my lord..."
Feminist criticism can focus either on her implied subordination to father and then husband or the independence and logic with which she makes her choices and presents her case.