How can I analyze Pygmalion through the critical lens of feminism?
Feminism looks at how women are perceived and what kind of opportunities they have in life. One of Henry Higgins' problems is that he can't see Eliza as fully human. Part of this is her class, but part of this is also her sex. For example, Higgins has an easier time not talking to Eliza's father, who is from Eliza's same lower class background, as if he is a child than he does Eliza. He insults Mr. Doolittle, but doesn't, for example, threaten to "wallop" him with a broom.
The play also takes aim at the way middle- and upper-class society denies "ladies" the opportunity for a career by making a key element of ladyhood not working for a living. At least the lower-class Eliza could earn her keep, poor as that keep was. As she so aptly says near the end of the play, "I sold flowers. I didn't sell myself. Now you've made a lady of me I'm not fit to sell anything else." Why, the play asks, are so many women not trained for anything other than marriage?