To understand the place Mary occupies in Catholic sensibilities, one must start with liturgy.
Mary is at the heart of Mass
There isn’t a mass where you won’t hear the name of Mary, either simply mentioned or called upon. She is often evoked as one of the “wonders” of Creation.
Mary is also held up as an example to evoke the fraternal communion of all humankind with God and the saints, which will be established at the end of times, a tenet of faith already anticipated in the Eucharist.
Finally we invoke her to recall her presence within the mystical body of Christ, reinforced by each worthy Holy Communion.
To evoke Mary during the celebration of the mass, even discretely, doesn’t just spring out of the necessity to remind ourselves of the fact that Christ is not an abstraction but a man born of a woman: it also manifests the fact that the Eucharist, as the celebration of God’s action on behalf of men through the Spirit, can’t be dissociated from Mary who is part of this action.
The third preface of the canon of the mass is an affirmation of this truth:
"Father all-powerful and ever-living God, we do well always and everywhere to give you thanks.
By the prophetic word of Elizabeth inspired by your Spirit, you manifest to us the greatness of the Virgin Mary, whom Elizabeth greets and proclaims truly blessed because she has believed, and in Mary’s service led by charity the mother of the Precursor recognizes the mother of the Lord.
This is why we join our voices joyfully to the canticle of Mary the Mother of God, and with all the choirs of angels and saints in heaven we humbly sing your glory and join in their unending hymn of praise: Holy, holy, holy...!”
The text of the preface is clear: Mary is the one who starts the song of praise to which all men join their voices.