What was John Stuart Mill's purpose for writing "The Subjection of Women"?

John Stuart Mill's purpose behind writing The Subjection of Women was to promote the advancement and happiness of humankind as a whole. Mill was advocating for women to be given the opportunity to reach their full potential—and for society to allow women to contribute as meaningful participants. In chapter 1, Mill himself states:

That the principle which regulates the existing social relations between the two sexes—the legal subordination of one sex to the other—is wrong itself, and now one of the chief hindrances to human improvement; and that it ought to be replaced by a principle of perfect equality, admitting no power or privilege on the one side, nor disability on the other.

This statement in his first chapter shows that he felt the current (for his time in the Victorian era) social practices of having men rule over women and make all of the decisions in society was outdated. Throughout the rest of The Subjection of Women, Mill discusses various ways in which the world as a whole would be a happier, better place if the genders were viewed as equals. He argues that all individuals should be eligible for a moral and intellectual education. Once that education was received, that individual should be able to participate in the society's functions, regardless of gender.