Civil, cultural, educational equality.
That's rather vague as a principle.
The right to vote, own property, be paid equally.
I believe the first two already exist. The third is more problematic, having to do with market forces and all.
To be not thought of as property of the husband,
Then you are for some sort of legislation which would impose thought and attitude controls on men?
to be protected from domestic violence,
In what way? We already have laws which do that. Would you have a police presence in every home 24/7 to ensure it?
to keep her own name if she so desires.
That has always been a matter of convention. By "her own name" do you not refer to the surname of her father?
For girls not to be automatically assumed "not as good at math as boys are" or that they should only do "girl things."
Who would automatically assume that, other than someone thoroughly ignorant of the human condition?
For women to be free to wear their hair the way they want or the clothes they want. (For example, some men think women shouldn't wear pants because they're dressing like men. Some men think women only wear dresses to draw attention to their sexuality.)
Then we must have some thought control legislation to prohibit "some men" from thinking the way they, perhaps, do?
To have access to and aspire to higher education without being held back by men who think women's roles should be domestic in nature only.
Those who aspire generally do, in my experience. My university experience was some 50 years ago and I don't remember any shortage of women in that setting. Far from it and I did attend a university with a significant student population.
As for the "fine the way they were" that would be before women achieved the civil, cultural and educational rights they now hold, although there still remains a culture of perception in some men which is evident here in this forum. One poster here believes "a few bruises" received from a husband isn't reason enough for the wife to seek divorce. Other men here don't believe women should vote. Still others denigrate women's rationality or blame them when they're victims of sexual harassment or assault.
Really? I believe your assessment of the civil and cultural climates extant are based on some amorphous view of assumed collective thought rather than on the merits of any individual case.
The above isn't comprehensive but it should give you an idea.
It does. And, I will give you the same advice I would, and have, given to others with a similar viewpoint as you. When one decides to trade power for status, be very, very, careful. As Shakespeare put it, "Uneasy lies the head that wears the crown."