I believe that although women and men in the Church do not have the same roles, we have divine responsibilities that are unique yet equally important. This is one of our fundamental doctrines. No, women have not been given the responsibility of the priesthood, but that is not because of a belief that men are somehow superior to women. The late prophet Gordon B. Hinkley said this about gender equality and women holding the priesthood:
“The men hold the priesthood, yes. But my wife is my companion. In this Church the man neither walks ahead of his wife nor behind his wife but at her side. They are co-equals in this life in a great enterprise.”
We have our own organization! And I have to tell you, it's amazing. I would elaborate more on what Gordon B. Hinkley said, but he said it very well so I'll leave it at that.
I'd also like to talk about how women are involved in the priesthood. This is a quote from lds.org:
To me, that is amazing. Men and women need each other to fulfill our divine roles. We can't do it without each other. Our roles are "different but equally valued."
So what are our divine roles? We've already touched on the priesthood portion of them. The Family: A Proclamation to the World outlines our roles perfectly. First we are designed to be parents and have a family. Then it says this: