I. "Woman" in the Vocative
One argument that we hear from contemporary Roman apologists is that when Jesus said, "Woman, what have I to do with thee," he wasn't scolding her, he was actually identifying her as the New Eve.
John 2:4 Jesus saith unto her, Woman, what have I to do with thee? mine hour is not yet come.
The more obvious explanation is that he is calling her "woman" rather "mother," to scold her. He was, in essence, denying her claim of maternal authority, by treating her as a stranger. Nevertheless, our friends in the Roman communion argue that this vocative case "woman" implies that Mary is the New Eve.
If that's so, there are at least least a few other New Eves:
1) Canaanite woman
Matthew 15:28 Then Jesus answered and said unto her, O woman, great is thy faith: be it unto thee even as thou wilt. And her daughter was made whole from that very hour.
2) Woman sick for 18 years
Luke 13:12 And when Jesus saw her, he called her to him, and said unto her, Woman, thou art loosed from thine infirmity.
3) Samaritan Woman
John 4:21 Jesus saith unto her, Woman, believe me, the hour cometh, when ye shall neither in this mountain, nor yet at Jerusalem, worship the Father.
4) Woman Caught in Adultery (This passage is still in Rome's Bibles)
John 8:10 When Jesus had lifted up himself, and saw none but the woman, he said unto her, Woman, where are those thine accusers? hath no man condemned thee?
5) Mary Magdalene
John 20:15 Jesus saith unto her, Woman, why weepest thou? whom seekest thou? She, supposing him to be the gardener, saith unto him, Sir, if thou have borne him hence, tell me where thou hast laid him, and I will take him away.
The better explanation is that the use of "woman" in the vocative is not a sign of being "new Eve," but rather is a way of addressing a woman one does not know. Compare the following uses by Peter and the angels (respectively):
Luke 22:57 And he denied him, saying, Woman, I know him not.
John 20:13 And they say unto her, Woman, why weepest thou? She saith unto them, Because they have taken away my Lord, and I know not where they have laid him.
It's perhaps not as gruff as in English (notice that not all the references above are negative, some are positive), but instead is a seemingly standard way of greeting a stranger.
Notice that in the garden, when Jesus says to Mary, "Woman ..." she thinks he's a stranger, but when he says to her, "Mary," she recognizes him.
Jesus saith unto her, "Woman, why weepest thou? whom seekest thou?"
She, supposing him to be the gardener, saith unto him, "Sir, if thou have borne him hence, tell me where thou hast laid him, and I will take him away."
Jesus saith unto her, "Mary."
She turned herself, and saith unto him, "Rabboni;" which is to say, "Master."
The non-acknowledgment of Mary at the wedding at Cana is similar to the non-acknowledgment of Mary's relation to Jesus, in Jesus' famous words to Mary from the cross:
John 19:26 When Jesus therefore saw his mother, and the disciple standing by, whom he loved, he saith unto his mother, Woman, behold thy son!
But the argument from Woman in the vocative case, as opposed to something more affectionate, like "Mary," or "Mother," is also informed by the context. In this case, the context is Jesus saying "what I have to do with thee!"
II. What have I to do with thee? (τί ἐμοὶ καὶ σοί" literally "what to me and to you")
This phrase, "τί ἐμοὶ καὶ σοί" (translated "what have I to do with thee") is really the more powerful of the two indicia that Jesus is scolding Mary. It is a Hebrew idiom that we see addressed to Jesus by the man possessed by the legion of demons:
Mark 5:7 And cried with a loud voice, and said, What have I to do with thee, Jesus, thou Son of the most high God? I adjure thee by God, that thou torment me not.
Luke 8:28 When he saw Jesus, he cried out, and fell down before him, and with a loud voice said, What have I to do with thee, Jesus, thou Son of God most high? I beseech thee, torment me not.
The corresponding Hebrew idiom is found (in several forms) in the following:
Judges 11:12 And Jephthah sent messengers unto the king of the children of Ammon, saying, What hast thou to do with me, that thou art come against me to fight in my land?
2 Samuel 16:10 And the king said, What have I to do with you, ye sons of Zeruiah? so let him curse, because the LORD hath said unto him, Curse David. Who shall then say, Wherefore hast thou done so?
2 Samuel 19:22 And David said, What have I to do with you, ye sons of Zeruiah, that ye should this day be adversaries unto me? shall there any man be put to death this day in Israel? for do not I know that I am this day king over Israel?
1 Kings 17:18 And she said unto Elijah, What have I to do with thee, O thou man of God? art thou come unto me to call my sin to remembrance, and to slay my son?
2 Kings 3:13 And Elisha said unto the king of Israel, What have I to do with thee? get thee to the prophets of thy father, and to the prophets of thy mother. And the king of Israel said unto him, Nay: for the LORD hath called these three kings together, to deliver them into the hand of Moab.
2 Chronicles 35:21 But he sent ambassadors to him, saying, What have I to do with thee, thou king of Judah? I come not against thee this day, but against the house wherewith I have war: for God commanded me to make haste: forbear thee from meddling with God, who is with me, that he destroy thee not.
Hosea 14:8 Ephraim shall say, What have I to do any more with idols? I have heard him, and observed him: I am like a green fir tree. From me is thy fruit found.
As you can see, this idiom is one that is used to distance oneself from others. Notice that in David's case, he is distancing himself from his nephews, the sons of his sister, Zeruiah (see 1 Chronicles 2:15-16). It's not a scolding or rebuke in itself, but when Jesus applies it to Mary, it suggests that his "Woman," comment is part of a theme of distancing himself from her.
He was rebuking her presumption in requesting a miracle when Jesus' time was not yet ready. He was not somehow giving honor or praise by this remark.