that we need bother about. (Act II)

Having thus dismissed Eliza's feelings, Higgins returns to concentrating on what he considers essential; namely, her grammar is atrocious and will be harder to correct than her pronunciation.

So often, he is guilty of this domineering superiority. Throughout the later acts, when Eliza becomes angry after he has gone too far with his impetuous bullying, Higgins employs coaxing cleverness rather than an apology to subdue her. It is only when Eliza takes a stand for her own dignity after the ambassador's party that Higgins begins to perceive Eliza no longer as a sort of millstone around his neck, but as a person who is deserving of his admiration. 

In the play Pygmalion, Professor Henry Higgins is a pragmatic professor of phonetics.  His sole "joy" in life is the study of linguistics and how it impacts human interaction.

He treats Eliza Doolittle as a component of an experiment. He is rude and short-tempered with her.  His impatience is not directed at anything she does or does not do, but at her mere mortality.  The agreement to tutor her is not so much to help her as it is to win a bet concerning his abilities.

He is successful in changing her dialect.  However, her attitude is also changed. In the process, she takes on the professor's attitude and that proves to be her undoing.

Though she is grateful for his time and energy, she can not tolerate his abysmal intolerance of humanity and eventually leaves his home.

Eliza and Higgins are characters who share a few things in common, and then drastically turn incompatible when specific events take place and shake the foundation of the scam that originally brings them together.

In both, Eliza and Higgins, we encounter two very passionate individuals who are quite safe within their own skin. They know who they are, and they are quite content with it. None of them believes that neither should be asked to change a thing about their personalities. In fact, the only reason why Eliza comes to get the phonetic lessons from Higgins is not because she isn't happy with herself, but because she looks forward to better work opportunities.

Eliza and Higgins are also stubborn, and assertive. They, unfortunately, also suffer from pugnacity when it comes to their anger. We see this in Acts 1, 4 and 5, particularly, where the dialogues in which Eliza and Higgins are involved are quite spiced, strong, and somewhat vituperous.

In contrast, Eliza is certainly a kinder and much humane than Higgins. She does show a certain quality of submissiveness when she pulls Higgins slippers, for example, and when she quietly listens to his rants. Eliza's feelings also get hurt several time in the play, which tells us that she is nevertheless a sentimental person who needs to feel appreciated. Eliza is no stranger to hard work, nor to a classicist society who view her as a lesser person. However, even with these elements have helped her develop a core of tolerance, she is still a tender person inside. Eliza is what we could compare to a modern day social survivor.

Higgins is an eternal bachelor. He is selfish in action, thought, and word. He is stubborn and inept for change. He is rash, bawdy, is oblivious to social decorum, and even to marginally adequate mannerisms. He seems so obsessed with his work that he has lost touched with his humanity, or that of others. He is hurtful, calculating, cold, and matter-of-fact. He is the anti-hero of melodrama; the epitome of the anti-romantic man. So much he is, that in the end he continues life as usual. This shows us the type of brash person he is that can only live for one instance of something that may or may not make a difference in his life.

In all Eliza and Higgins's similarities are what make their differences so powerfully charged when they argue and disagree. This is what makes for great drama in a play, and perhaps a great technique employed by Shaw to demonstrate the uniqueness of his characters.

Eliza has learned to have a sense of self worth by the end of the play. She has succeeded at becoming a lady, despite her working-class origins.

This leads her to two realizations. First, she learns that by becoming a lady, she has unfitted herself for earning her own living. All a respectable lady can do is get married. Whereas before, it was perfectly reasonable for her to earn a living selling flowers, money-making would now destroy her new status. She chafes under this restraint, thinking it senseless.

Second, she realizes she can stand up to Henry Higgins. She no longer needs to put up with his arrogant commands and ceaseless verbal abuse. She does challenge him, showing she is fully human and demanding he acknowledge that, which surprises him greatly.

Eliza grows in self-esteem and assertiveness as a result of her experiences.

Absolutely.  For one thing, Higgins takes on Eliza as a student due to a dare with a friend.  Higgins, without regard for Eliza as a person at all, takes the dare that he can make her speak like Royalty so well that no one will detect the fraud in very little time.

For another thing, Eliza and Higgins come from two very different backgrounds and social classes.  Neither truly understands the other, although Eliza is a good student and she learns quite a bit more than the speaking patterns in her crash course.  Regardless, her "new" self leaves her in limbo--she doesn't fit in her old world, and she doesn't really fit into the new one either.

Higgins never expects or plans for emotions.  He approaches everything from the perspective of an experiment.  It doesn't work that way when people are involved.  His mother points this out, as does Pickering and Eliza herself.

One might be tempted to say that the pig-headed Henry Higgins learned nothing from Eliza Doolittle, but that's not entirely true. While he continues to treat her rudely and orders her around as if she is his errand-girl, by the end of the play he has developed a grudging admiration for her newfound spunk. She is no longer afraid to fight back against him. He says, "I like you like this." He also praises her strength of character. He even tells her she is throwing herself away on Freddie, saying she could marry a king if she wanted.

Higgins also expresses surprise when Eliza informs him that she learned how to be a lady from Pickering's example, not from Higgins, indicating that Eliza's good opinion means something to him. 

In the end, Higgins has, in fact, brought a statue to life, as in the original Greek myth: Eliza becomes her own person, independent of her "creator." His behavior may not change, but he has possibly developed an awareness that Eliza is a human being, not just an experiment in linguistics.