In contrast, relations between people of opposite genders are generally portrayed by Shaw as antagonistic. From his unusual standpoint of being committed to a celibate marriage, Shaw apparently feels free to denounce marriage as an exchange of sexuality for money similar to prostitution even though this was not happening in his own marriage.
This means more than a mere distinction between rich and poor. Pygmalion created a sculpture of a perfect woman and fell in love with it; after he prayed, Aphrodite brought it to life for him. Shaw in some sense pits their intellectual intelligence against the wits of others, like Eliza. This statue is named Galatea, and it is represented in Shaw's play by Liza.
He of course has nothing to lose since he has money, fame, and position. Shaw makes clear that transformation of the flower girl is not the stuff of myth, but a necessary part of modern life, where social justice is part of the ongoing process of human history.
He is lower class but understands how the game is played and disdains to take part. She declares that she was less degraded as a flower-seller than as a "genteel" lady trying to make an appropriate marriage--because as a flower-seller, at least, she wasn't selling her body.
There were ways of rising to a higher class, through education, money, or marriage, but those were exceptions.