I believe what you state is only a piece of the much larger puzzle. And as stated above just having a signal piece is easily dismissed, in this case,by stating equality.
The large picture, which this is just a piece, is we are all one family, the human family. We are to be able to come together as a family. As such anyone you meet, male or female, is a member of your family and should be treated as such.
So women are not just to be treated as your mother/grandmother/sister, but men are to be treated as your father/grandfather/brother. I would add to that list daughter/granddaughter and son/grandson respectively. In all that there is the potential for a mate as well, as that is one of the driving forces of the human family.
It is recognition of this who this person is first, what are the family relationships that exist between you both, then seeing where it leads that I see is the answer. Is their agreement in this between both - if not there that is something to consider.
Also just to add that I also believe we are a very mixed up family and it is not uncommon for a person to have muti-family roles in each others lives, in some instances you can be a parent to them, others them to you, other times you can both be as small 'sibling like' children, other times adults to each other.
To that I have found in romantic relationships it is usually better to find a person that you can connect on all those 4 levels (adult/adult,parent/child,child/parent,child/child) and that takes time to find out, and it takes experiences and does take respecting the human family, all it's members including yourself - and by respecting yourself and the family and members you will respect the other person.
Peace