If you believe that women face oppression and/or discrimination, it is necessary to have language to identify that and to address it. I don't know what it means to root someone's identity in her physical characteristics but there is certainly a material reality about being a woman and a political structure that treats a person in a particular way because she is a woman. It's important for women to be able to discuss these things.
This is the World Health Organisation's definition of sex and gender:
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"Sex" refers to the biological and physiological characteristics that define men and women.
"Gender" refers to the socially constructed roles, behaviours, activities, and attributes that a given society considers appropriate for men and women.
To put it another way:
"Male" and "female" are sex categories, while "masculine" and "feminine" are gender categories.
Aspects of sex will not vary substantially between different human societies, while aspects of gender may vary greatly.
Some examples of sex characteristics :
Women menstruate while men do not
Men have testicles while women do not
Women have developed breasts that are usually capable of lactating, while men have not
Men generally have more massive bones than women
Some examples of gender characteristics :
In the United States (and most other countries), women earn significantly less money than men for similar work
In Viet Nam, many more men than women smoke, as female smoking has not traditionally been considered appropriate
In Saudi Arabia men are allowed to drive cars while women are not
In most of the world, women do more housework than men
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