Stepping into the shoes of one of my Protestant friends with whom I've enjoyed thought-provoking conversations over our respective Christian faiths, I asked "Why?" with regard to the last part of the paragraph, which reads:
But the Blessed Virgin's salutary influence on men originates not in any inner necessity but in the disposition of God. It flows forth from the superabundance of the merits of Christ, rests on his mediation, depends entirely on it and draws all its power from it. It does not hinder in any way the immediate union of the faithful with Christ but on the contrary fosters it (emphasis added).There are many reasons to venerate Mary, the Mother of God, but I was just not getting why she would or could foster my union with Christ if I already believed in her son. What is the point?
I don't have the memory to be able to quote my classmates verbatim, but suffice it to say, what resonated with me was, just as God may use any believer in his plans to "mediate" between Him and other believers or non-believers, God also uses Mary. In other words, by my living out my faith in even the most seemingly mundane aspect of my life, I may knowingly, or unknowingly, help someone in their relationship with the Lord. It may be their initial exposure to someone following the will of God, or it may be just the something they needed to return to God after a loss of faith, or maybe something that further solidifies their faith.
Consider Mary's response to being told by an angle of the Lord that she was full of grace and would bear the Son of God, "Behold, I am the handmaid of the Lord. May it be done to me according to thy word" (Lk 1:38). If knowing of someone who surrendered themselves to the will of God helps foster, or mediates, a relationship with Christ for another, there isn't a greater example than Mary.