From the Cross, Jesus gave his mother to John and thus to all of us.
No, He specifically gave Mary to John and John to Mary.
There is NOTHING in that passage that lends itself to the interpretation that Catholicism gives it.
Look, Rufus' mother is the mother of us all! She is even more humble than Mary, we don't even know her name but you can bet that she was immaculately conceived and is the queen of heaven. She hears our prayers and intercedes with Jesus and He must listen to her because she is the mother of us all.