The first instance,...
The topic of "dependence of men" is illustrated in George Bernard Shaw's Pygmalion in two ways: women are dependent on men because they have no choice, and, women are dependent on men but do not need to be if they do not wish to.
The first instance, the theme of women being dependent because they have no choice is illustrated at the beginning of the play in the dynamics of the Eynsford Hills. Mrs. Eynsford Hill and her daughter, Clara, follow the Victorian propriety of allowing "the male" take care of them, in this case, the man of the house is Frederick Eynsford Hill, the elder brother of Clara. However, he is not the type of man that neither his mother, nor his sister, would be entirely proud of. He is a bit weak of mind, body, and character. He is also not extremely bright. Evidence of this is illustrated in the way that he is treated when he, as the man, is unable to find a cab for his mother and sister.
THE MOTHER: You really are very helpless, Freddy. Go again; and don't come back until you have found a cab.
FREDDY: I shall simply get soaked for nothing.
THE DAUGHTER: And what about us? Are we to stay here all night in this draught, with next to nothing on. You selfish pig—
Hence, we can assume that the women are only dependent on him because that is what society has taught them to do.
The second statement, women are dependent on men but do not need to be if they do not wish to,is illustrated in Eliza's dynamics with both Fredrick and Higgins. As a woman who always did for herself, Eliza has always had a choice on whether to need or not to need. When she meets Fredrick she appreciates the fact that he is devoted to her. However, she knows that she cannot count on him too much.
Eliza's desire to have Freddy in the house with her seemed of no more importance than if she had wanted an extra piece of bedroom furniture.
We also learn about how things go in their marriage, and after their attempt to open a flower shop.
Freddy, like all youths educated at cheap, pretentious, and thoroughly inefficient schools, knew a little Latin. It was very little, but enough to make him appear to her a Porson or Bentley, and to put him at his ease with botanical nomenclature. Unfortunately he knew nothing else; and Eliza, though she could count money up to eighteen shillings or so, and had acquired a certain familiarity with the language of Milton from her struggles to qualify herself for winning Higgins's bet, could not write out a bill without utterly disgracing the establishment.
Meanwhile, with Higgins, at one point Eliza really thinks that the natural course of their relationship would be to be married. However, she realizes that Higgins has no inkling for love and she much rather be his competitor, his challenger, rather than his amiable companion and his dependent.
LIZA: [with sudden sincerity] I don't care how you treat me. I don't mind your swearing at me. I don't mind a black eye: I've had one before this. But [standing up and facing him] I won't be passed over.
HIGGINS: Then get out of my way; for I won't stop for you. You talk about me as if I were a motor bus.
LIZA: So you are a motor bus: all bounce and go, and no consideration for anyone. But I can do without you: don't think I can't.
And she is right! In the end, Liza gets her way and it is she who carries the stronger character, dealing with life, work, home, and Higgins as well, as a peer. She chooses not to depend on anybody.