It's a sweet-sounding sentiment. One that I hear just about every year around Mother's Day, which I most recently read on facebook, posted by a friend who is very sweet and kind, very well-intended, and very wrong.
All women are NOT mothers.
It is true that when God made women he gave us the capacity for nurturing, and many women are very good at that, including many who are not yet mothers. It is true that women with no children (biological, adoptive, step, or other) contribute in many important ways to the nurturing of and caring for other's children. But this does not make them Mothers.
Pretending otherwise belittles the pain felt by the woman who longs for children, but is unable to bear them.
Pretending otherwise belittles the hurt and longing felt by women who, waiting for honorable marriage, can have no children.
Pretending that all women are Mothers belittles and diminishes the tremendous eternal significance of the work that mothers do. It is saying that even those who have no children are doing the very same thing, contributing in the very same way. It is not so. Childless women contribute. But they are not Mothers, and they are not doing the same things.
When the Lord sends a child to a family, He is giving those parents a sacred trust and responsibility. He also gives parents authority sufficient to carry out their responsibilities. He will require an accounting from parents for the raising of their children. While Aunts, Sisters, Grandmothers, and other female friends may assist, that responsibility remains upon parents. A mother is a Mother to her own, and none else.
The calling of father or mother is sacred and carries with it great significance. One of the greatest privileges and responsibilities given to us is that of being a parent—helping to bring to earth a child of God and having the sacred responsibility to love, care, and guide children back to our Heavenly Father. In many ways earthly parents represent their Heavenly Father in the process of nurturing, loving, caring, and teaching children.
-Robert D. Hales
Women without children simply don't have this privilege or responsibility. What they do have is the promise that no blessing will be withheld for lack of opportunity in this life. They have the assurance that the Lord who sees the desires of their hearts will hear and answer their prayers.
He maketh the barren woman to keep house, and to be a joyful mother of children. Praise ye the Lord.