Catholics give great honor to Mary of Nazareth and venerate her under the title of Mother of God. In brief the reasons can be stated in this way:
(1) We are dealing here with a work of the Creator who is unlimited in power and has within Himself existence. This Infinite Being is not just a force; it is Wisdom and Truth. Since this Creator is the source of being for anything that exists there is nothing beyond its hand; and only nothing is beyond His hand.
He has revealed Himself as Love. His very essence is to love.
He has revealed Himself as a Trinity of Persons.

(2) The Second Person of the Blessed Trinity entered into his own creation as the Word of God incarnated in the man Jesus of Nazareth.
Jesus was killed because he told us that he was Divine and also a human (John 5). This Incarnation is completely opaque to any creature but it is a reality which He proved by rising from the dead three days after he was crucified ( John 20; Paul 1 Cor. 15).
(3) Since Jesus is a Divine person who is truly one with the Trinity, that means that He chose Mary of Nazareth to be his personal temple. The Trinity itself — all reality == all truth — lived for 9 months in the womb of this creature.

(4) Every woman is a holy thing because it is in women that the Creator carries out His act of Creation. Thus women and sexuality are really sacred and should be treated that way. Unfortunately we have degraded this wonderful gift of womanhood into a plaything and an object of our lust.
(5) The woman Mary, however, since she held the most pure Creator in her womb could never have been an enemy of God at any time. This is why Catholics call her Immaculate and Ever Virgin)

(6) If she was and is Immaculate, then she is one of four humans formed that way by the Hand of the Creator: Adam, Eve, Mary and Jesus. The first two sinned and thus lost this gift of belonging only to the Creator. Jesus, of course is Divine and could not sin even though he has free Will.

Thus, Mary of Nazareth is the unique human being who has never had the slightest shadow of belonging to anything or anyone except the Creator.
This, of course, has to be accomplished by the Grace of God. Since she is the one creature perfect in God’s grace she is a unique creature who perfectly carries out the Will of the Creator.
Thus we venerate and honor this unique Creature. Not to do so would be to impute that the power of the Creator is limited.
I think that one of the principle reasons Protestants have a difficult time accepting this is that, at the heart of their faith they have a difficulty (unspoken) with the Incarnation. It seems to me that began with Luther. A major argument of his to which the Protestant Divines subscribe to is that the Roman Catholic Church, to which was entrusted the Keys of the Kingdom went astray and that the Protestant Reformation is an attempt to return to the pristine faith of the Apostles.

However, this betrays a lack of belief in the Divinity of this man Jesus. Because, it is obvious, that if He truly is God and He gave birth to the Church with his death on Calvary, He certainly would have the power to keep His Church (Mathew 16) faithful to His teaching and to His Will. The only way that the Catholic Church could have gone astray is if Jesus was only human, because He said that the powers of hell would not prevail against His Church and that He would be with it until the end of the World (Matthew 16; 28).
For the Catholic, however, there is a more cogent fact. Each of us sees her , not so much as this exalted person, but as a kind and compassionate mother who cares for each of us. She, as you know, is the mother of Christ and this includes His members (Ephesians 1). We, who are baptized into Christ, are baptized by the Holy Spirit of God which Jesus gave to His Church when he died. She loved and cared for Jesus as her son — and we being linked to her Son by the perfect bond of Divine Love, she also loves and cares for us.
It is absolutely true that never was it known that anyone who fled to her protection , implored her help ,or sought her intersession ,was left unaided.