In The Great Gatsby, what does Daisy mean when she says this: "And I hope she'll be a fool—that's the best thing a girl can be in this world, a beautiful little fool."
In this context, Daisy suggests that she hopes her daughter is a fool. Daisy expresses a defeatist attitude. She implies that women have a difficult role to play in the world, so the best chance for her daughter to be happy is to accept the traditional role of subservient woman. Essentially, in this case, Daisy is hoping her daughter is ignorant because ignorance is bliss. If her daughter is unintelligent, she won't know how the world really works and/or that there are alternatives to marrying people like Tom.
It is important to note that when her daughter is born, Tom is not there.
It’ll show you how I’ve gotten to feel about—things. Well, she was less than an hour old and Tom was God knows where. I woke up out of the ether with an utterly abandoned feeling, and asked the nurse right away if it was a boy or a girl. She told me it was a girl, and so I turned my head away and wept.
Later in the novel, Daisy reveals that Tom has had affairs (in addition to his affair with Myrtle Wilson). We, readers, can only speculate as to where Tom is at the time of his daughter's birth, but even if he isn't off having an affair, he is still negligent for not being there.
Instead of hoping that her daughter will be self-reliant and able to make informed decisions (and hopefully avoiding marrying someone like Tom), Daisy feels defeated and pathetically hopes that her daughter will be happy in her ignorance.
This quote is taken from chapter one when Daisy is telling Nick about the birth of her daughter.
Through this quote, Daisy makes an important point about 1920s American society. Specifically, she notes how society views women and their role in the world. Daisy hopes her daughter will be "beautiful," implying that society only values women who are physically attractive. Moreover, by hoping that her daughter is a "fool," Daisy also acknowledges that her society does not care about the intellectual capabilities of women. In fact, her society prefers women to be intellectually inferior.
Daisy understands that her society is a patriarchal one in which there is no place for a woman who is both self-aware and intelligent. This suggests that Daisy has direct experience with the sexist treatment of women, experience which has contributed to her character and view of the world.
Finally, it is also worth noting that Daisy does not challenge this sexism. In fact, she accepts the world for what it is and hopes that her daughter will come to understand these aspects of society. In her opinion, this realization is the "best" way, and this gives Daisy's comment a sad and despairing tone.