The root of the new feminisim boils down to the early centuries when women were ridiculed in the society. Women were treated as plain housewives who would just stay in their houses, take care of their husbands and children. Moreover, they are deprived of rights such as voting or employment. Men were dominant over women that's why they are more privileged.
In the modern times, the society has evolved. Women today are treated almost equally as men. Women can now vote, have their own career while still taking care of their families. The goal of new feminism is to give the women the same rights as the men. They do not aim to dominate over men. All they want is equality among all genders.