To understand Our Lady’s direct role in our salvation, we must go back to the Garden of Eden. You have there a Paradise, you have a man and a woman, you have a tree, you have a bad angel.
The man and woman were without parents and were the parents of all. They were the greatest of all human beings, and were created in a state of original justice, i.e. the state of grace.
You have the devil gaining a great victory over Adam, by two means: a tree and a woman. The woman leads the man to the tree and the tree begets death for the man. The devil deceived the woman and the woman caused the man to sin out of human respect.
As a result, these first parents become the authors of death. They are able to communicate physical life, but with that physical life comes the sentence of physical death and immediate spiritual death, since all of their children are born in Original Sin.
From the first sin of the first parents comes all the succeeding sins of mankind. We may say that Original Sin was the origin of the “culture of death.” Spiritual death leads to physical death. The next story in Scripture is the murder of Abel by Cain. And the murders and other crimes just go on from there, until we reach our present day world, where millions are slaughtered.
Now, God decided from all eternity to overturn sin by making a complete reversal of the scene in the Garden, such that the work of Redemption is sometimes called “the Divine Revenge.”
At the very moment of the Fall (from the human point of view, because God sees all simultaneously in eternity), God issues a decree for its remedy. For this remedy to be a Divine Revenge, He needs a man, a woman, and a tree. Just as He intervened in the Creation of the first Adam and Eve, so will He have to intervene for the second Adam and Eve. Consider how He accomplishes His revenge.
You have a man and a woman without spiritual parents. Our Lady was conceived without Original Sin, and thus she was created in grace by an operation of the Holy Ghost. Our Lord as well had a Conception in the plenitude of grace. These two are the only ones in the history of the world, besides Adam and Eve, created in a state of original justice.
Adam came into the world without a father. Our Lord came into the world without a father.
Original Sin was committed by means of a tree and a woman. The woman was deceived by the devil and the fruit of the tree was death. Thus, it was fitting that Original Sin was defeated by means of a tree and a woman. Our Lady brought Our Lord into the world and led Him to the tree of the Cross. The first tree brought forth spiritual death; this tree brings forth physical death, but spiritual life. To this day, we cannot be saved without the Cross and Our Lady.
Eve, Mother of all the living, is the source of physical life for all, but also spiritual (and physical) death. Original Sin comes from Adam, but passes through the womb of Eve for any to receive it. As such, God gave Our Lady the role of being the physical mother of Our Lord and the spiritual mother of all who are born again in the life of grace. All who live that life must pass, as it were, through her womb.
From Adam and Eve come the fallen human race. From Our Lord and Our Lady come the redeemed human race.