What was Pygmalion's conflict?

Pygmalion explores class conflict. In a class-bound society like England, a conflict raged: was social class inborn or socially constructed? In other words, were people from the lower classes genetically inferior, incapable of learning the gracious behavior of upper class people, or had they been held down and "coarsened" by their lack of economic opportunities? Were they naturally "depraved" or had they been made that way? 
Henry Higgins sets out to prove that he can pass off a lower-class Cockney flower girl, Eliza Doolittle, as an aristocratic lady by teaching her to speak proper English, instructing her in manners, and dressing her as an upper-class woman. 
Higgins succeeds, perhaps beyond his dreams, and in the process, upends popular misconceptions in 1913 about social class, showing that it is nurture (or lack thereof), not nature, that keeps people down. Upper class people are not innately superior. Higgins, however, can never quite get over his class prejudices, or his sexism, and thus can never treat Eliza fully as a human being. Shaw's play, therefore,  not only upsets the idea that the upper classes are naturally (genetically) superior but calls into the question the careless and often destructive way women and lower-class people were treated. 
Pygmalion's conflict at the end of the play that Eliza is caught between marriage, the only role she is fitted for now that she is a lady, and her own desire for independence and autonomy.