How we cite our quotes:
HIGGINS. Pickering: shall we ask this baggage to sit down or shall we throw her out of the window? (2.30)
Judging Eliza by her slovenly appearance, Higgins treats Eliza like an object instead of a human being. His comment is no doubt sarcastic, but it tells us something about his attitude toward women.
LIZA. I ain't got no mother. Her that turned me out was my sixth stepmother. But I done without them. And I'm a good girl, I am. (2.118)
Eliza seems to have grown up without a feminine presence in her life, and she's proud to have turned out all right anyway. Perhaps this pride is what leads her to keep claiming she's a "good girl."
HIGGINS. Oh, pay her whatever is necessary: put it down in the housekeeping book. [Impatiently] What on earth will she want with money? She'll have her food and her clothes. She'll only drink if you give her money.
LIZA [turning on him] Oh you are a brute. It's a lie: nobody ever saw the sign of liquor on me. [She goes back to her chair and plants herself there defiantly]. (2.121-122)
Higgins stereotypes Eliza as a poor person and simply assumes that she has a drinking problem.