Stephen: may I ask how soon you intend to realize that you are a grown-up man, and that I am only a woman? (1.15)
Lady B is playing at needing Stephen's advice. She claims to be "only a woman," but don't be fooled—she's in charge during the whole convo about family finances, and she expects to stay that way.
There may have been some reason for it when the Undershafts could only marry women in their own class, whose sons were not fit to govern great estates. But there could be no excuse for passing over my son. (1.61)
Here, Lady Brit is musing over her husband's power to make decisions for their family—big ones—without her consent. Even though she's making a big show about how it would be unacceptable to have "her son" passed over, ultimately her husband (as convention demands) will make the call.
Barbara: you have had the education of a lady. Please let your father see that; and don't talk like a street girl. (1.181)
Lady Brit seems a bit dismayed by her daughter's behavior upon seeing her father for the first time in years, wanting to make sure Andrew can see that she has brought Barbara up as a "lady." It probably seems old fashioned to readers now, but apparently that was a reasonable thing to be concerned about in turn-of-the-century England.
The others do. That is the injustice of a woman's lot. A woman has to bring up her children; and that means to restrain them, to deny them things they want, to set them tasks, to punish them when they do wrong, to do all the unpleasant things. And then the father, who has nothing to do but pet them and spoil them, comes in when all her work is done and steals their affection from her. (1.260)
As fun as we find Lady Brit, and as much as she seems large and in charge for most of the play, the reality is that she does end up getting kind of a raw deal in the end; no one really listens to her, and the kids basically all end up going over to Undershaft's views. So, her reflections here about the unfairness of a woman's lot seem kind of foreshadow-y.
That's what's so unfair to us women. Your confessions is just as big lies as ours: you don't tell what you really done no more than us; but you men can tell your lies right out at the meetins and be made much of for it; while the sort o confessions we az to make az to be wispered to one lady at a time. It ain't right, spite of all their piety. (2.27)
Beginning with a statement that kind of echoes Lady B's complaints about the lot women face (see elsewhere in this section), Rummy is bitter about the existence of different standards for ladies and men. Of course, she's mostly upset because these standards get in the way of her ability to lie to others and thereby win their sympathy.
Yes: you like an old man to hit, don't you, when you've finished with the women. I ain't seen you hit a young one yet. (2.65)
Peter Shirley, another man at the Army shelter, is telling off Bill Walker for basically only wanting to pick on people who aren't his size. Bill and his opinions about women (which let's just say aren't exactly progressive) get a lot of airtime in Act II.
Somebody that doesn't intend you to smash women's faces, I suppose. Somebody or something that wants to make a man of you. (2.187)
When Bill asks who other than Barbara could possibly be trying to "get to him," she points the finger squarely at God. While making the hard sell in an effort to convert him, she tries to appeal to his sense of manliness . . . and perhaps remind him that hitting women isn't particularly manly.
A mite o mawn last week ed words with the judye's gowing to merry. E give er wot-for; an e's bin fawnd fifteen bob. E ed a rawt to itt er cause they was gowin to be merrid; but Aw edn't nao rawt to itt you; sao put anather fawv bob on an call it a pahnd's worth. [He produces a sovereign]. Eah's the manney. Tike it; and let's ev no more o your forgivin an prying and your Mijor jawrin me. Let wot Aw dan be dan and pide for; and let there be a end of it. (2.361)
Bill seems to be (bumblingly) trying to make up for hitting Jenny Hill . . . but along the way, he lets drop that he thinks his friend who got in trouble with the law for hitting his girlfriend ("judy" is slang for girlfriend) was totally in the right in what he did. In his view, since the girlfriend was about to be his friend's wife, that made it okay. As you can see, Bill's moral compass is pretty busted. Or missing altogether.
Power to burn women's houses down and kill their sons and tear their husbands to pieces. (3.408)
When Barbara is lamenting the terrible power of her father's weapons, her thoughts turn immediately to the impact on women and their houses, sons, and husbands. It's interesting, since she could have just talked about destruction in general and the deaths of men on the battlefield, but she made it first and foremost about women's losses. Hmm, why do you think she goes there?
Like all young men, you greatly exaggerate the difference between one young woman and another. (3.351)
This is Undershaft's charming comment when Dolly is trying to figure out whether to take over the Undershaft family business, even though it means he might not get to be with Barbara (who has previously disapproved of her father's trade). Even though Barbara is his daughter, Undershaft seems to suggest that no woman—not even his daughter—is worth giving up this opportunity, since according to him, they're all the same. Uh, okay.