I. The Church PersonifiedNow, the Church is frequently personified in Scripture. Paul shows us the Church as the Bride of Christ, and refers to Her as "Her," in Ephesians 5:22-32,
Wives, submit yourselves to your own husbands as you do to the Lord. For the husband is the head of the wife as Christ is the Head of the Church, His Body, of which He is the Savior. Now as the Church submits to Christ, so also wives should submit to their husbands in everything.
Husbands, love your wives, just as Christ loved the Church and gave Himself up for Her to make Her holy, cleansing Her by the washing with water through the word, and to present Her to Himself as a radiant Church, without stain or wrinkle or any other blemish, but holy and blameless. In this same way, husbands ought to love their wives as their own bodies. He who loves his wife loves himself. After all, no one ever hated their own body, but they feed and care for their body, just as Christ does the Church— for we are members of His Body. “For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh.”[Genesis 2:24] This is a profound mystery—but I am talking about Christ and the church.If you notice, Paul paints a picture of the Church as the Bride of Christ, and as the Body of Christ, and even as Something indistinguishable from Christ (since "He who loves His Wife loves Himself," Eph. 5:28).
II. Mary as MotherIn John 19:25-27, one of the last things Jesus does on the Cross before dying is give Mary as Mother to the Beloved Disciple:
Near the cross of Jesus stood his mother, his mother’s sister, Mary the wife of Clopas, and Mary Magdalene. When Jesus saw his mother there, and the disciple whom he loved standing nearby, he said to her, “Woman, here is your son,” and to the disciple, “Here is your mother.” From that time on, this disciple took her into his home.Now, the Catholic understanding of John's Gospel is that John is presenting himself as the Beloved Disciple, not to gloat about the favor he found with Christ, but to present himself as a model. That all of us should act as beloved disciples of Christ. If this is true, then Christ from the Cross is giving His Mother to all of us. Note also that He refers to Her as "Woman." This is going to be really important in looking at Revelation 12.
III. The Kicker: Revelation 12The single most important passage to know in understanding why Catholics say things like "Mother Mary" and "Mother Church" is Revelation 12. Here's Rev. 12:1-2, 5:
A great sign appeared in heaven: a Woman clothed with the sun, with the moon under Her feet and a crown of twelve stars on Her head. She was pregnant and cried out in pain as She was about to give birth. [...] She gave birth to a Son, a Male Child, who “will rule all the nations with an iron scepter.” [Psalm 2:9]The Son, obviously, is Christ. But what about the Woman? There are two major theories: that the Woman is Mary, and that the Woman is Israel and the Church. Now, Catholics affirm both, but it seems that everyone would have to affirm at least one of these.
We think it's Mary for obvious reasons. First of all, She gave birth to Christ. So taking the vision on face, Mary's an obvious choice. Second, She's referred to in the New Testament simply as "Woman." This is because of Her role as the New Eve. Eve, before the Fall, was simply known as "Woman." Mary, being preserved from original sin, is the New Eve, and from Her flesh and bones God draws the "Last Adam" (1 Corinthians 15:45). All of this is foretold in Genesis 3:15, which promises that a Woman will bear Seed, and that the Child of this Woman will crush the head of Satan. It's this prophesy which Christ references on the Cross in John 19.
But it's also Israel and the Church. Jesus Christ, as King of the Jews, is the culmination of Israel - the very drawing apart of a Jewish people was, for all time, for this purpose. Genesis 12:3 shows that Abraham's lineage was to be a blessing for every people on Earth, and through Christ, this blessing is fulfilled. The Church of Christ, then, is the fulfillment of Israel, and Romans 2:29 shows us this quite plainly. The old priesthood gave way to the New, just as the old Law gave way to the New (Hebrews 7:12), and so on. We see this also in the picture of the Woman in Revelation. We see twelve stars, symbolizing the twelve tribes of the Old Testament, which culminate in the twelve Apostles of the New (see Matthew 19:28).
Interestingly, the details which are mentioned in Revelation 12 seem to signal that both conclusions are intended. For example, Rev. 12:6 says that the Woman fled to the wilderness, for a place prepared Her by God. This is a reference to the journey of Israel and his family travelling to Egypt in Genesis 46, but it's also a reference to Mary and Her family going into Egypt in Matthew 2:13-15. In both cases, God specially prepared a place for them (sending Joseph ahead of Israel in Genesis; and sending an angel to instruct St. Joseph in Matthew).
Now, why is this all so important? Look at how Revelation 12 ends. This is Revelation 12:17 -
Then the dragon was enraged at the woman and went off to wage war against the rest of her offspring—those who keep God’s commands and hold fast their testimony about Jesus.Two things to notice. First, this directly links back to Genesis 3:15, which promises enmity between Satan (represented there as a snake, and here as a dragon) and the Woman, who we know to be Mary If you read the two, and then read the instances in John 2 and John 19 in which Jesus calls Mary "Woman," a very clear picture starts to form. Namely, that in Genesis 3, God promises that Mary and the Devil will be mortal foes, and that Mary will give birth to Christ, who will crush the head of Satan.
This is actually a bit shocking - the Bible is saying that Satan hates Mary. It's not what we might assume - I mean, of course he hates God, but Mary? Here, I think the understanding of Mary that many Protestants have renders this passage nearly nonsensical. Mary, to many Protestants, is no different than any other believer: a fallen, even totally depraved, sinner who just happened to have been in the right place at the right time to become Jesus' Mom. But that's emphatically not how the Bible is portraying Her: She's part of a cosmic battle. According to this passage, the Devil goes after you and I because He wants to hurt Her.
But there's a second thing to draw from this passage, almost too obvious to dwell on. True believers in Christ are depicted as children of the Woman. Now, Protestants might think that the Woman is Mary, but not the Church, or the Church, but not Mary, but ultimately, I think you have to take at least one of the two readings. The Woman refers to Someone and/or Something. And that Someone or Something is Our Mother.
So if you read this chapter as referring to Mary, then Rev. 12:17 tells us that Her offspring are all "those who keep God's commands and hold fast their testimony about Jesus." She is, in other words, the Mother of the Living spiritually, as Eve was mother of the living by the flesh (Genesis 3:20). So calling Her "Mother Mary" is only fitting, since Scripture says She's our Mom. On the other hand, if you read the chapter as referring to the Church, then using the same logic, Mother Church is a fitting title. In fact, to deny that the Church is our Mother would be to deny that you are one of the faithful of Rev. 12:17. Or, in St. Cyprian's words, "No one can have God as Father who does not have the Church as Mother." Or, if you're aware that both Mary and the Church are described, then both titles are fitting.