Shaw's Pygmalion satirizes the social snobbery of the late Victorian era by focusing on speech and manners. Professor Higgins, though born well, stands outside the social conventions by his willingness to mock and dismiss everything that he does not like. What he does like is language and the way the articulation of vowels marks on by locale. In England, locale also marks one by class, and then as now, it can be very hard in England to move across class lines, even when one accumulates wealth. Class was considered a product of breeding, of superior genes, and of taste. Like Higgins, Shaw found that idea preposterous.
Higgins embarks on a process of intense and accelerated study that involves changing Eliza's articulation and, in the process, her manners. She is exposed to lovelier things than she has ever been able to afford and begins to prefer them; thus her taste changes too.
However, the biggest change in Eliza comes not simply in being able to speak, dress, and behave like an English genteel woman but in being perceived as one. When she is offered respect and dignity, she and the audience see the difference in how the class system works to keep classes separate, with false understandings of inferiority and superiority.
Eliza's father also speaks to this on moral grounds, suggesting that the poor are too impoverished to live by the standards of "middle class morality." Only those too poor to afford morals or too rich to care are given a kind of social freedom that fosters independence.