Nobody objects to a woman being a good writer or sculptor or geneticist if at the same time she manages to be a good wife, a good mother, good-looking, good-tempered, well-dressed, well-groomed, and unaggressive.
What is asserted by a man is an opinion; what is asserted by a woman is opinionated. A woman with ideas and the ability to express them is something of a social embarrassment, like an unhousebroken pet.