Out of a history where women have consistently been disadvantaged on account of their sex, women's rights is embraced as a critical agenda by most people aspiring for a truly democratic society - this, as a matter of basic human rights. What exactly this means and looks like differs across political communities.
In the progressive view of women’s rights - often known as feminism - any roles women might freely choose should be respected and supported. Furthermore, we may insist that no barriers on the basis of gender alone should be permitted under the law. Just as civil rights have been expanded over the life of our American democracy (through laws and court decisions) e.g. to former slaves, native Americans and the Civil Rights Act prohibits sex discrimination as well as race, national origin - so also the Equal Rights Amendment is intended to prevent exceptions from being created/recognized. From this vantage point, women should have the same right as men to pursue life liberty and happiness - at home, in the workplace and in society. If so, many distinctions currently allowed cannot be justified.
For conservatives, the traditional roles of women are typically focused primarily on home, children and caregiving as natural and fulfilling. From this vantage point, feminism has often devalued roles that are essential foundations to human life and of the highest dignity. Feminism also is seen as putting women's rights in opposition to men's rights - in a zero-sum game where there can only be one winner. This is seen as undermining natural relationships between men and women that are important for the strength of families and the society.
That being said, conservatives insist they are not opposed to fundamental women’s rights - with legal equality like voting and the right to own property appropriate rights to insure to women. But when it comes to arguments like "equal pay", and the mandate of what has been tried and failed - an Equal Rights Amendment to the Constitution - conservatives see this as forcing the same treatment of men and women where it should not be - eg military service and the military draft. This also disrespects the traditional roles of women which are not recognized as at times justifying certain differentiations in the treatment of men and women that are intended to protect these traditional roles.
The question of what creates equality has continued to be an interesting conversations Feminists tend to argue that paid maternity leave and accommodations to women's unique reproductive role - and sometimes, to their physique - should be viewed as part of "women's rights." By contrast, conservatives tend to argue that equal is equal - women have to compete on the same ground as men.