Patriarchy does not permit those equalities Ophelia.
Going to get accused of mansplaining feminism here, but I answered because I was asked.
I would say, from what I understand, that patriarchy does not allow those equalities by dehumanising women in two principal respects. Firstly, it defines them as the fairer sex. The fairer sex are programmed by God or nature to be compassionate, peaceable, nurturing and passive. As well as primarily existing to produce and care for children, the fairer sex embody a sacred progenitive energy (The Sacred Feminine; The Earth Mother). But they're not just mothers, they're also objects of romantic infatuation, placed on pedestals and sought as prizes by men who are partly bestial. All men are born with a violent libidinal energy that is only countervailed by their desire for the spiritual purity represented by the sacred Madonna. As for the Madonna, she has no libidinal energy, violent or otherwise; she has no rationality so cannot do great deeds; she has no capacity for evil, so cannot do evil ones. She is nothing but voiceless passivity, purity and virtue. The man hates this virtue because he can never attain it, tormented as he is by his evil lusts - lusts which he directs at the Madonna's counterpart: the whore.
While the Madonna, is pure passive virtue, the whore is passive vice. She is pure viscera, dirt, death. An object onto which male sexual hatred can be projected.
All of this is obviously wrong. Women are not born meek, passive and nurturing; and neither are they whores. They are human beings, and vary hugely from individual to individual. And neither are men born with all these destructive sexual neuroses. All these things are engineered - through social and economic processes.
Neither men nor women are in any innate sense different or better than one another. Indeed, as distinctions of value, male and female have as much meaning as blue-eyed and brown-eyed.