It's not even close.
Yes, I realize all this.
Were you baptized as a Catholic and then you became a Protestant, or were you born into a Protestant family ?
Paragraph 6. Mary - Mother of Christ, Mother of the Church
963 Since the Virgin Mary's role in the mystery of Christ and the Spirit has been treated, it is fitting now to consider her place in the mystery of the Church. "The Virgin Mary . . . is acknowledged and honored as being truly the Mother of God and of the redeemer. . . . She is 'clearly the mother of the members of Christ' . . . since she has by her charity joined in bringing about the birth of believers in the Church, who are members of its head."502 "Mary, Mother of Christ, Mother of the Church."503
If it was just a personal arrangement between three people, why do you suppose it was recorded in the Gospel? (See John 20:31)
John was the "disciple whom Jesus loved," and the Greek says that he took Mary "eis ta idia" = "To his own" people, place, etc.
As I say, it's not just a personal arrangement, but symbolizes something much bigger. It's not for nothing that John's Gospel begins with the wedding feast of Cana (Mary: "Do whatever he tells you") and ends with John taking Mary "eis ta idia".