Not so. The genitive as used here is just a possessive in an exchange between three people, Jesus, Mary and John. It is only showing a new relationship between John and Mary. It does not exclude other possible relationships. See Mark 6:3 for the use of the possessive applied to Jesus' brothers.
Peace,
SR
Actually, the changing use of the genitive is excellently demonstrated here to make the Catholic point of view.
οá½Îº οὗτός á¼ÏƒÏ„ιν ὠτέκτων ὠυἱὸς ΜαÏίας ἀδελφὸς δὲ Ἰακώβου καὶ Ἰωσῆ καὶ Ἰούδα καὶ Σίμωνος
The genitive exists before “Maria,” but not before “adelphos.”
Because while James, Josa, Juda and Simon have many brothers, Mary has only one child.
Even the Greek Orthodox who refuse to accept that adelphos is a mere translation of an Aramaic word, and so insist that James, Joseph, Judas and Simon are brothers of Christ, nonetheless they insist that Mary has only one child. The others, they reason, must be children of Joseph from a previous marriage.