Power and words
Butler's arguments show that language is ironically powerful. Though words seem to be secondary, they are primary. Through language, beliefs are formed, and once formed, those beliefs are manifested in the culture. She explains how this process of building social constructs through language is powerful, and if there is to be change in power, there must first be change in language. She details the differences between words and their associations, starting with "women" and "woman," where negative statements about women tend to use women, and where positive statements tend to use woman.
Nature as a judge
The book appeals to nature in several occasions showing that although one might suspect animals are inherently sexist (which is an important point for this debate), the truth from nature is that animals tend not to demonstrate the social gender roles that we humans do. Whether this is good biology or not has been the subject of many debates, but the ironic truth is that humans are animals, but because of language, we can deviate from nature through social construction.
Weakness as programmed
The painful irony of Butler's feminism is that women are actually chronically weaker than men, but not because of any inherent deficit. The problem in reality is that women are not typically educated about power. Not only that; they are also chronically unlikely to be curious about power because until a girl sees women in power, it is less likely that she will understand in a serious way that she could obtain power in society. There is an injustice here, because women are not taught to reach their full potential.
The irony of patriarchy
Although there are many ironies concerning patriarchy, the irony that Butler identifies most clearly is that patriarchies seem natural because in our animal species, men are clearly stronger by nature. However, this is not true at all, she says. Ideas about masculinity and femininity, and ideas about gender role are not actually rooted in nature. Rather, modern gender roles are derived from the social constructs of the past; patriarchy stems from early man subjecting woman to his power in a system that perpetuates itself.
The supportive role
For various reasons, the typical belief has been that men should work and women should stay home, but Butler observes that this is simply nonsense. The irony of this role is that it seems so clearly true, because this is the belief that has been demonstrated en masse in modern Western culture, but she writes that there is more than one way to raise a family. The man can stay home, and nothing explodes, and no one dies, and the woman can earn money, and the sun doesn't fall out of the sky. The ideas are purely hypothetical, and in this case, the gender roles are dangerously limiting.