The Virgin Mary is our mother because we are the mystical body of Jesus Christ (1 Corinthians 12:27) and Mary is the mother of that Jesus whom we are members of. The body cannot be separated from its Head (Col 2:19).
On Saul’s (later St. Paul) way to Damascus in order to persecute Christians, Jesus said to him: “Why do you persecute ME?” (Acts 9:4). Jesus did not say “Why do you persecute “my people”, or “my followers”, but “ME”. For to Jesus, His followers are considered “Himself”. Therefore, since Mary is His mother, she is also the mother of those who love and follow Jesus. It is because of this revelation on his way to Damascus that St. Paul understood that Jesus’ Church is His Body and started to write about it. This is also the reason why, before dying on the Cross, Jesus said to the “disciple whom he loved”, “Behold your mother”.
“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.” (John 19:26-27 – NIV).
This Gospel was written by the Apostle St. John, and it was to him whom Jesus told “behold your mother”; but notice that it is not written that it was to “John” or “I” or “me”, but “the disciple whom he loved” – it is a general description. It is because this has a deeper message or meaning which goes beyond the historical facts. This is a teaching. Jesus, dying on the Cross, gives His mother to the disciple whom He loves. This is personal. St. John was not bragging about himself at this particular passage, but it is a teaching on to whom Jesus gives His mother, and that is any disciple who “takes her into his or her home”. It doesn’t say “John took her home”, but “this disciple”. Notice that it doesn’t even say “this Apostle” (for that’s what St. John actually was concretely speaking) but instead it says “this disciple”. The Apostles (capital “A”) were the ones who were sent by Jesus personally. “Apostle” (from the Greek “apóstolos”) in the strict sense means “the one who is sent off”, but “disciple” applies to us all who “follow” Jesus. So we can adequately take advantage of this gift from God, His mother.
Also, it is a Commandment of God to honor our father and our mother (Exodus 20:12).