Pretty much in this one, Eliza is super upset that the men in her life aren’t giving credit for her hardwork, and when she lets slip that she won higgin’s bet, he gets really mad because he thinks that because she is a woman, she is just a test subject, a guinee pig if you like. 

Higgins thinks that because she is a woman, she gets spontaneously emotional, like the stigma of because a woman has her period, she gets super emotional. So he is trying to calm her down and make her feel batter,but he is doing it in such a way that is sexist, but I dont think he knows it.

Higgins’ treatment of Eliza can easily be likened to that of a master and a servant. He relies on her, almost childishly, to remember his own appointments and possessions that he should be responsible for, as an adult, to manage.
Mrs Higgins, almost reminding Higgins, that Eliza is a person with rights to herself and she can come and go as she pleases. 

Higgins does not take Eliza into consideration, does not want to waste anything good of his on her.

Pickering and Higgins reported Eliza to the police, knowing full-well that she left of her own will and intent. This pursuit after Eliza is like a pursuit after lost property- which Mrs Higgins scolds them for. 
Higgins and Pickering were fully aware that Eliza left of her own will and intent, and so their pursuit after her is childlike and foolish- and can be perceived as an intrusion into Eliza’s privacy.

After this quote, Eliza is saying that she doesnt know what to do after she leaves, because everything she owns, where she lives, whats shes learnt, its all from Higgins. She doesnt know how to be herself, or how to be her new self 

This quote is super sexist because Higgins is saying that because Eliza is beautiful, all she is good for is marriage. Nowhere in this act does he draw light on her exceptional intelligence, as she pretty much learns how to speak and act completely different to how she does already. He only ever draws on her looks and her failures.  

Not only does this refer to Marxism, but feminism. There is no distinction between whether he is discriminating her class or her gender, still he is being extremely rude and treating her like she is worth nothing

- Higgins.

 
Yes, it's short and doesn't mean much. But like really Higgins? You just picked up a girl? Objectification in my opinion. I bite my thumb at Higgins

- Higgin

Eliza picks up on the fact that she’s being treated badly and Higgins is objectifying her to dirt, and before it was a bag. She does not like the way she has been treated and makes it loud and clear that she has been treated that way.

Once again, to him, women are all under categories and not individuals. They're all 'idiots'. 

Higgins protest against Doolittle caring and providing for Eliza stems from the basis that he ‘bought her’. However, Eliza is a person, not a product or an object that can be bought in a shop.

Then again.

Here Higgins brings Eliza's worth down to a dog as he demands her to sit and do as she’s told. She is treated like a dog should be treated. Which is wrong and horrible altogether.

- Higgins.

OK, so she's following orders. Nice. Just nice. Speaks for itself I think.

She makes a fair point here, like when she was purely herself, doing her own thing, being a florist queen, she didnt have to worry about the male gaze, and about how others wanted her to act. Now that she does, she doesnt know what to do with herself. She never turned to prostitution on the streets because she knew that she didnt want to do that, so she didnt. However, now that she is a lady, all she see’s herself fit as, and what she has been told, is that she is only there to be on the arm of man.

Mrs Pearce is now stuck in the loop of that men are higher than women (maybe also in class too) because Higgins has treated her like he is treating Eliza, but she’s become used to it that she doesn’t pick it up.

Mrs Higgins sympathises with Eliza’s situation. As a woman of status and a member of the upper class, she is accustomed to a comfortable living situation. However, as a woman, she understands Eliza’s situation in not receiving the recognition she so rightly deserves. 
Her outrage at Higgin’s ignorance in the matter is rightly justified as she is able to sympathise with Eliza on a level neither Pickering nor Higgins could hope to achieve.

Higgins refers to her as dirt once again.

Grr.. "Ladylike"

She puts it down how it is. She was just an experiment, they wanted to see if a female could learn how to be the ideal woman. She did it, she won his bet. But why is she getting no credit? Because she’s a female, thats why.