You are aware that if in one fictional day women and girls just magically be transferred to another planet where there's no man, the women will pick up all the works, right? Same applies to men too!
And, the meaning of the phrase "women don't need men" is not "women don't need men in the planet". It's just that many women are tired of all the dramas and a relationship with men under this world wide system of patriatchy. Hence it'll be really nice to live on the same planet but not get into any relationships. You are unknowingly or deliberately misinterpreting the meaning.