Shaw does not believe that men are superior to women, and he does exaggerate Professor Higgins's dialogue in act V in order to highlight the idiocy of what he has to say.
By act V, Eliza has more than proven her worth. She has convinced the aristocrats that she is indeed a high-born lady. She has fought with Higgins over the way he treats her and has thrown his slippers in his face. In every way, she has shown herself a competent, intelligent person, and she is distressed that Henry cannot bring himself to treat her as a full human being because of her class background.
In act V, Eliza, who has taken shelter with Henry's mother, confronts Henry about his cruelty. Rather than understanding her point of view, he belittles her, saying,
"You call me a brute because you couldn't buy a claim on me by fetching my slippers . . ."
Eliza tells him that her intent was not to "buy a claim" and states that it is not dress or accent that makes a lady, but being treated with respect. Nevertheless, Higgins has a virtually impossible time understanding that he owes her anything or that she is anything more than the flower girl he found on the streets. Shaw is critiquing Henry's attitude as cold-hearted, snobbish, and narrow-minded.