In the book Brave New World, how is it shown that freedom is more important than happiness?

Huxley argues that freedom is more important than happiness by presenting John the Savage as a sympathetic, honorable character, who is opposed to the superficial, shallow culture of the World State. In the World State, the entire society is void of discomfort, danger, pain, and inefficiency. Citizens are scientifically manufactured, and the society is divided into five castes. Conformity, happiness, and stability are the cornerstones of the World State. Despite this efficiency, comfort, and convenience, however, citizens' lives are completely controlled by the government, and the technologically advanced society lacks important elements of the human experience, like spontaneity, creativity, art, love, and spirituality. The citizens of the World State are portrayed as superficial, ignorant, and shallow. Many characters, like Lenina Crowne and Linda, rely on soma to suppress their negative feelings and happily conform to the shallow culture of the World State.
In this manufactured world, John the Savage is an outcast, who vehemently opposes everything the World State represents. In a moving debate with Mustapha Mond, John argues for the essential elements of humanity, which make life spontaneous, exhilarating, and stimulating. Huxley purposely creates sympathy for John's character, who desires freedom over comfort and happiness. For John, freedom is the ability to live a daring life, where he can worship as he pleases and form deep emotional bonds with others. John values the opportunity to make independent choices and experience the world without oppressive government interference. John's outlook on life and his desire to live a free, spontaneous life are depicted as noble and worthy. When John is juxtaposed with the shallow citizens of the World State, his convictions and lifestyle seem superior. Through John's character and outlook on life, Huxley suggests that freedom is more important than happiness.

Huxley gives us a picture of a world in which the ordinary problems of life as we know it have seemingly been eliminated through scientific planning and the use of drugs. But selective breeding results in people's characteristics, and thus their activities in life, being predetermined, established in advance for them without freedom of choice. For the most part, however, the population of the dystopia do not see themselves as lacking freedom. There are the occasional "misfits" such as Bernard and Helmholtz, but in general the society functions as it is intended to.
This fact, however, the presence of even a couple of malcontents (which is a typical element of dystopian fiction) shows the system is flawed and that even the kind of freedom its own people believe in is illusory. That some parts of the world (like the "Savage Reservation" where John is born) have survived from the pre-dystopian epoch is probably meant by Huxley to show that ultimately, no system in which human happiness is dependent on science can ever become universal. Because man himself is flawed, any system he devises is also flawed and has within itself the seeds of its own downfall.
Though the dystopia he presents is a kind of hedonistic perfect world in which most people have a lot of fun, to put it simply, from our point of view it leaves out the things we value most, such as love, commitment, and the spiritual component of life. By presenting the character of John as a foil, Huxley drives this point home—that the kind of freedom and happiness we know and desire is absent from this sterile world. But because it is a world from which pain and the ordinary messiness of life are absent, one cannot escape the impression that Huxley, and all of us who are his readers, would have some degree of ambivalence about these issues.