Edit: Chad has written his interpretation of this passage here with slightly alternative views.
Edit 2: I’ve done some extensive thinking on this topic and I actually believe Chad’s version is closer to correct now. I will leave this up as the lessons this post teaches are still applicable even though my analysis of the Scripture may be slightly off.
The marriage at Cana is the first miracle of Jesus per the testimony of John, and another interaction between Jesus and his mother.
If we remember back to Jesus in the temple, this is his interaction between his mother, Mary, and himself:
Mary: “[s]Son, why have You treated us this way? Behold, Your father and I [t]have been anxiously looking for You.
Jesus: “Why is it that you were looking for Me? Did you not know that I had to be in My Father’s [u]house?”
Instead of getting sucked into his mother’s opinion of what He was doing, Jesus reframes the issue into one of what God wanted him to be doing. This is one example of where answering a question with a question allows Jesus to redirect the conversation towards spiritual things rather than earthly things. Away from his mother’s concerns, and towards the Father’s concerns.
However, even in this situation, Jesus submits to his parents — His earthly authorities — so as to be in full obedience to the law of Moses and to His Father in heaven.
Now, let’s move on to the marriage at Cana in John 2 (NASB)
On the third day there was a wedding in Cana of Galilee, and the mother of Jesus was there; 2 and both Jesus and His disciples were invited to the wedding. 3 When the wine ran out, the mother of Jesus *said to Him, “They have no wine.” 4 And Jesus *said to her, “Woman, [a]what does that have to do with us? My hour has not yet come.” 5 His mother *said to the servants, “Whatever He says to you, do it.” 6 Now there were six stone waterpots set there for the Jewish custom of purification, containing [b]twenty or thirty gallons each. 7 Jesus *said to them, “Fill the waterpots with water.” So they filled them up to the brim. 8 And He *said to them, “Draw some out now and take it to the [c]headwaiter.” So they took it to him. 9 When the headwaiter tasted the water which had become wine, and did not know where it came from (but the servants who had drawn the water knew), the headwaiter *called the bridegroom, 10 and *said to him, “Every man serves the good wine first, and when the people have [d]drunk freely, then he serves the poorer wine; but you have kept the good wine until now.” 11 This beginning of His [e]signs Jesus did in Cana of Galilee, and manifested His glory, and His disciples believed in Him. 12 After this He went down to Capernaum, He and His mother and His brothers and His disciples; and they stayed there a few days.
The first concept we see in this passage at the wedding is that there is a problem. What does Mary do when they find out there’s a problem?
3 When the wine ran out, the mother of Jesus *said to Him, “They have no wine.”
She indirectly asks Jesus to fix the problem.
Now, I don’t know if she asked politely with good manners, but telling a man about a problem which implies that He fix the problem tends to be disrespectful in most cultures. However, I won’t say that it was sinful or disrespectfully because I don’t know, and I don’t want to call good evil or evil good.
Thus, Jesus replies curtly:
4 And Jesus *said to her, “Woman, [a]what does that have to do with us? My hour has not yet come.”
Jesus addresses other women by the term “woman” in the gospels, and this was not uncommon in the culture. However, it seems that most commentaries agree that it would be disrespectful for a man to address his mother as such.
Analysis from Wiki — Mary told Jesus the wine was in short supply. Today his reply may seem curt: “Woman, what have I to do with you? My hour is not yet come.”[Jn. 2:4] Neither here nor elsewhere does Jesus renounce the mother-son relationship as such, but here, as in Luke 2:49, he declares his vocational (ministerial) independence of his mother.
He has an “hour” to meet, and Mary, though his mother, can neither hasten nor hinder its coming.:pp.103–104, 236 Most scholars believe that in Jesus’ reply to his mother there was no disrespect. According to Matthew Henry’s Commentary, he used the same word when speaking to Mary with affection from the cross. Scholar Lyn M. Bechtel disagrees with this reading. She writes that the use of the word “woman” in reference to Jesus’ mother is “startling. Although it would not be improper or disrespectful to address an ordinary woman in this way (as he often does: see John 4:21, 8:10, 20:13-15), it is inappropriate to call his mother ‘woman'” (Bechtel 1997, p. 249). Bechtel further argues that this is a device Jesus uses to distance himself from Judaism.
However, Bishop William Temple says there is no English phrase that represents the original “Woman, leave me to myself.” “In the Greek it is perfectly respectful and can even be tender—as in John 19:27…. We have no corresponding term; ‘lady’ is precious, and ‘madam’ is formal. So we must translate simply and let the context give the tone.” Some versions of the Bible translate it as “Dear woman”. 
The commentaries, unfortunately, do not look at Jesus’ actions in light of male-female relationships or even mention Mary’s prior comment which prompted the curt reply from Jesus.
The curt reply of Jesus was to address Mary’s incomplete picture of the situation at hand.
Looking in the context of male-female relationships and conversation this could have two different meanings:
“Woman, [a]what does that have to do with us? My hour has not yet come.”
- An exasperated Jesus replying as to a child that was testing his patience, “Come on, what does that have to do with us?” or “Why are you telling me to fix someone else’s problem?”
- An amused Jesus replying perhaps with a raised eyebrow, “So what? What does that have to do with us?”
When Jesus was at the temple, Mary was concerned about Him but Jesus redirected the attention off of her worry onto the fact that He had to go about His Father’s business. It was an excellent redirection of the situation with another question, yet He still obeyed His parents and returned with them.
In this case, whether Jesus was exasperated or amused or something else, He was still in control of the situation by responding to Mary’s assertion with another question. The type of reply Jesus made addresses Mary’s incomplete picture of the entire situation which was twofold: (1) taking an issue that wasn’t their problem and potentially making it their problem, and (2) not thinking about the consequences of said actions.
In other words, Jesus redirected Mary’s statement from concern over the present into Spiritual matters again. Otherwise He would have just said “Okay mother, I’ll turn some water into wine”.
Likewise, this is a great lesson for husbands, as wives and women often bring problems up to husbands to fix. This is neither good or bad in itself, but sometimes the problems focus merely on the physical and ignore the spiritual. Or they didn’t consider the consequences of said actions.
However, after Jesus redirected Mary’s statement from earthly things to heavenly things, He does acquiesce and perform a miracle:
5 His mother *said to the servants, “Whatever He says to you, do it.” 6 Now there were six stone waterpots set there for the Jewish custom of purification, containing [b]twenty or thirty gallons each. 7 Jesus *said to them, “Fill the waterpots with water.” So they filled them up to the brim. 8 And He *said to them, “Draw some out now and take it to the [c]headwaiter.” So they took it to him. 9 When the headwaiter tasted the water which had become wine, and did not know where it came from (but the servants who had drawn the water knew), the headwaiter *called the bridegroom, 10 and *said to him, “Every man serves the good wine first, and when the people have [d]drunk freely, then he serves the poorer wine; but you have kept the good wine until now.” 11 This beginning of His [e]signs Jesus did in Cana of Galilee, and manifested His glory, and His disciples believed in Him. 12 After this He went down to Capernaum, He and His mother and His brothers and His disciples; and they stayed there a few days.
edit: Thanks to Chad for pointing it out some of the corrections above, and prayer about changing parts of this post were Spirit inspired.
The key point in this passage is Jesus’ immaculate concern of the Spiritual over the physical. He doesn’t fall into the trap of pleasing those at the marriage or women, even his mother, but rather addresses her concern over a problem by curtly telling her the long term implications of such actions. We should be reminded to focus on spiritual as opposed to earthly things, and that all actions have consequences.
In terms of male-female relationships, winnowing out intentions is important as well as consideration of the Spiritual over the physical. These are both characteristics of masculinity in interacting with women: to reveal the intentions or truth behind women requests and to evaluate them in light of the Spirit and consequences that may result.
Mark 4:21 And He was saying to them, “A lamp is not brought to be put under a [e]basket, is it, or under a bed? Is it not brought to be put on the lampstand? 22 For nothing is hidden, except to be revealed; nor has anything been secret, but that it would come to light. 23 If anyone has ears to hear, let him hear.”
Luke 8:16 “Now no one after lighting a lamp covers it over with a container, or puts it under a bed; but he puts it on a lampstand, so that those who come in may see the light. 17 For nothing is hidden that will not become evident, nor anything secret that will not be known and come to light. 18 So take care how you listen; for whoever has, to him more shall be given; and whoever does not have, even what he [e]thinks he has shall be taken away from him.”
Likewise, one of the other lessons men can learn from this is that women, even your mother, are going to demand or tell men do things all the time to fix their problems or to fix someone else’s problem. Mary was essentially volunteered Jesus’ time and energy to fix a problem that was not His problem.
As you may recall, this is the same concept behind which I wrote Christian nice guys are abused [for their time].
Husbands and men should call out women for volunteering or telling them to do things. These are things that should be discussed by the husband before a decision is made. A wife volunteering time without asking her husband is not respectful behavior.
Key point for wives/women: Ask politely, don’t tell men to do things. Don’t abuse men to do things for you.
Key point for husbands/men: If women don’t respect you and your time then call them out on it. It may be good to do the things that wives/women are bringing up to you as Jesus acquiesced and performed a miracle, but you must ensure that women are respectful of your boundaries as men by calling them out on disrespectful behavior.
Key point for all: Focus not just on the physical or earthly things but the Spiritual ramifications of actions. Indeed, consider both the action and the consequences of said action in light of the Spirit and not the flesh.