God gave His command (to subdue the earth) to both Adam and Eve, not just to Adam. While “headship” rests with the man, the calling is to both people and neither are a second class citizen. Not at all. The calling is for both Adam and Eve as a couple…
Both men and women were created in His image and he called both “man” in Gen 1.
Then God said, “Let us make man in our image, after our likeness. And let them have dominion over the fish of the sea and over the birds of the heavens and over the livestock and over all the earth and over every creeping thing that creeps on the earth.” So God created man in his own image, in the image of God he created him; male and female he created them. – Gen 1:26-27
God created man (both men and women) in his own image, in the image of God he created him;
male and female he created them. And God blessed them. And God said to them, “Be fruitful and multiply and fill the earth and subdue it and have dominion over the fish of the sea and over the birds of the heavens and over every living thing that moves on the earth.” And God said, “Behold, I have given you every plant yielding seed that is on the face of all the earth, and every tree with seed in its fruit. You shall have them for food. And to every beast of the earth and to every bird of the heavens and to everything that creeps on the earth, everything that has the breath of life, I have given every green plant for food.” And it was so. – Gen 1:27-30
So clearly the male man is not the only one to be given dominion.
Equal, but to be handled very differently
Certainly God treats men and women differently, we can see that in the way he speaks to them and what He says to them.
But the command to have dominion in Gen 1, the initial instruction given, the overall plan, was given to both.
There is no greater or lesser, just different roles both working towards a goal given to the couple. Not greater or lesser, but indeed there are different roles, because God designed us differently.
He made us for a purpose and things work better if we adopt the roles He has given us.