John Stuart Mill is a man, explaining why he feels that feminism is an important path forward for society. This means that he is admitting to privilege, but instead of getting some sort of white savior complex, he simply explains what knowledge is available to him through his point of view. He uses his enfranchisement to enfranchise those points of view which he feels have been systemically disenfranchised by the majority.
For women, Mill's arguments are intuitive and obvious, but Mill is a man, which means that if he had wished, he could easily have made use of the privileges pertaining to his manhood (in his societal context, this is unignorably true, and this entire book is him elaborating about how true that is in his personal experience). But instead, he speaks openly from a kind of common sense, urging others to take a forward-thinking stance.
This means that he is both conservative and liberal at the same time, because he appreciates the value of the enfranchisement he uses, but he observes that technically, it is only superstition and archaic points of view that perpetuate the myth that women are inferior. The crux of his argument is airtight, logically speaking; it would be simply unfounded to pretend that women are being supported to meet their full potential. If men are so confident that they are better, why not allow the women a truly fair chance to compete? They would have nothing to lose, says Mill, and if they are wrong, it will be better for everyone, since women will finally be allowed to thrive.
