I'm about halfway through the latest volume of Luther's Works (Sermons on the Gospel of St. John Chapters 17-20). In reading Luther, I enjoy his sermons the most. This volume is a wonderful collection of insight, exhortation, and the Gospel.
Commenting on John 19:25-27 ("Woman, behold, this is your son!".... then he said to the disciple, "Behold this is your mother!"), on pages 261-263, Luther says, "Deservedly, Mary is our mother." I've quoted this source, Roman Catholic style: no context.
But there is a context, and I have it. Unfortunately, it doesn't do much to expound on exactly what Luther means, but we still can compare it to something like this: Mary is Our Mother, Catholic Online. In this contemporary article, "Mary is our mother" means the following:
1. The Virgin Mary is a personal, spiritual mother. Only recognizing her as our true Spiritual Mother will lead to an authentic response to Mary. Roman Catholics love, revere, and honor her and seek her intercession and protection. In the human family, a mother is not optional. So too, in the spiritual family of the Mystical Body of Christ, Mary, our Mother is not optional.
2. In John 19:25-27, John is symbolic of all humanity. When Jesus says, "Behold your mother" this means Jesus from the Cross gave His Mother to every human person for all time. Mary doesn't become our mother, she is our mother, and we are her children. Jesus is the head of the body of believers. So, if she gave birth to the head, she must have given birth to the entire body of believers.
3. A mother doesn't give birth to a child only to abandon the child. She nurtures, feeds, teaches, guides, and protects her child. God entrusts Mary with these tasks. Mary's children should turn to her confidently with love and devotion for protection, guidance, and assistance in their hours of gravest need. To do this, is to do as Jesus did. She had given birth to Him, nurtured, fed, guided, and protected Him. To put our trust and confidence in her will always be pleasing to God because everything she does will always lead us closer to Him.
Now with this in mind, here's Luther's words from his 1529 sermon:
The dear Lord Christ wants to say His final farewell to the world and depart from it entirely. He has nothing else on earth, neither money nor possessions, neither tunic nor clothing; rather, He hangs bare upon the cross. He has nowhere to lay His head, neither has He even a foot of earth upon which to die. He is not lying on a bed but hangs suspended in the air. He has only His mother and His most beloved disciple. Now He departs from the world altogether and gives away His mother and His most beloved disciple, who reclined on His breast at the Last Supper [John 13:23]. It is immensely painful when someone departs in this way and refuses to concern himself any longer with either mother or disciple or anything else on earth. The dear Lord must think no good of the world to give it such a complete farewell.
To His mother He says, "Woman, behold, this is your son." To the disciple He says: "Behold, this is your mother." And from that hour the disciple took her to himself. That is as much as to say that John the disciple took Jesus' mother as his own mother, took her into his home, looked after her and cared for her, and provided for her so that she had a place where she could stay as a solitary widow now robbed even of her only Son.
In the papacy, Mary was made into an idol on the basis of this text. Even in the Passion, when they preached about Christ and His sufferings, they preached about the mother, Mary, namely, that she has been given and committed to us by Christ to be our mother. We want to hold the dear Virgin and holy mother in all honor, as she certainly deserves to be honored. Yet we will not so honor her as to make her equal to her Son, Christ. For she was not crucified nor did she die for us; neither did she pray for us on the cross. But it was Christ who was crucified and died for us and with tears offered supplications and prayer for us on the cross [Heb. 5:7]. Therefore, let each one honor the mother Mary as he will—provided only she is not honored with the honor due to Christ. And this is also the reason why the Lord separates His mother from Himself: so that He will be the only one to whom we should cling.
But the pope with his monks does the opposite, sending Christ the Son away and clinging to the mother. Christ abandons everything for our sake—the earth, His mother, His disciples—in order to save us. Therefore, we should cling to Him alone and give the honor that is due Him to no one else. For since He Himself gives His mother away and does not want to be with her on earth, 'nor to cling to her, neither should we cling to the mother and forsake the Son. Deservedly, Mary is our mother. But if we wanted to rely upon her, taking away Christ's honor and office and giving them to His mother, that would be a denial of the sufferings of Christ.
So, does Luther mean the same thing as "Catholic Online"? Hardly. Luther opposed Romanist idolatry then, and not much has changed.
By the way, lest anyone think Luther often said "Mary is our mother," the editors of Luther's Works say, "In (apparently) the only other place in which Luther affirms the formula that Mary is "our mother," it is in connection with Christmas and the Christian's identification with the Christ Child: see sermon for Christmas Day, December 25, 1530, WA 29:655."