Is the desire for a spiritual mother natural to mankind? I've been answering a few questions on this site raised about the intercessory power of the  Blessed Virgin Mary and this question popped into my mind.  St. Thomas Aquinas can posit a rational proof for God's existence, glory, omnipresence, omniscience, eternal nature and beneficence.  I don't think he ever said, God exists because &quot;we need Him&quot;.  But, He does exist and it's reasonable to say the He doesn't need us.
But, there is a sensitivity that is natural to man that brings him closer to God, to want to know what we can about Him.

Now creatures lead us to the knowledge of God, as effects do to their cause. Accordingly, by natural reason we can know of God that only which of necessity belongs to Him as the principle of things.
Summa Theologica Book 1, Article 32

Since Christ's death and resurrection, the Catholic laity has had an ardent devotion to the Mother of God and also consider her to be the mother of the Church and their own spiritual mother.  The truths which Sacred Tradition kept through constant devotion to Our Lady (i.e. The Immaculate Conception and the Assumption) are considered by the present Pope and the popes who promulgated said dogmas to be infallible (that's saying something coming from the Pope).
So, here's the question, if we can know God through reason alone, is it also reasonable that God willed that we have a maternal queen in Heaven as well who acts as a spiritual mother?
Looking for Catholic answers rooted in the Natural Law
In his book, First Comes Love, Scott Hahn outlines a concept of God that is in concert to this question.  He cites a writing of Pope John Paul II.


  “In the light of the New Testament it is possible to discern how the primordial model of the family is to be sought in God Himself, in the Trinitarian mystery of His life.  The divine “We” is the eternal pattern of the human “we”, especially of that “we” formed by the man and woman created in the divine image and likeness…God in His deepest mystery is not a solitude, but a family, since He has in Himself fatherhood, son-ship and the essence of the family, which is love.”


Hahn concluded:


  “Now we must be very careful readers here, because many people understand these statements precisely backward, which mans they don’t understand them at all.  The Pope was not saying that God is like a family.  He was not presenting the family as a cozy, homey metaphor for the Trinity.  He said that God is a family.  Thus, it would be more accurate to say that my wife, my kids, and I are like a family than to say God is like a family.  God is not like a family.  He is a family.  From eternity, God alone possesses the essential attributes of a family, and the Trinity alone possesses them in their perfection.  Earthly households have these attributes, but only by analogy and imperfectly.”


God's creation tells us that a Father has a Wife and a Son has a Mother as well as a 
Father.  The Holy Spirit bears fruit from the will of God the Father and the First-Fruit is Jesus Christ.  

The Hebrew word “Ruwach” is a feminine noun, therefore when Jesus spoke of the Holy Ruwach He understood that spirit by nature is feminine. 

The Holy Spirit overshadowed Mary, which is eternally pregnant with the will of God the Father.  Just as Mary the mother of the incarnation we also through the overshadowing of the Holy Spirit bear out the will of God the Father in our lives, which is Jesus Christ.

So "yes", The Holy Spirit is Mother, the Church is Mother and Mary is Mother!