First, the word translated "wine" in English (οινου in Koiné Greek) can refer to either alcoholic or non-alcoholic wine. Today, the term "wine" is used exclusively for alcoholic wine, but let us never be guilty of interpretation based solely upon modern day definitions. We must remember every time one sees the word “wine”, the context determines whether alcoholic or non-alcoholic grape juice.
The immediate context of John 2:1-11 is quite clear. The guests at the marriage feast of Cana were able to discern between the quality of the drink that the Lord had made and that which had already been served. If intoxicating wine had been served, and people were "well drunk" then they would not have had such keen discernment. Being well drunk is like being well-fed, and simply means they have had plenty. Though the amount is not specified as to what they had previously drunk, if they consumed the six waterpots that Jesus had the servants fill with water and which contained "two or three firkins apiece" (verse 6), then they would have consumed somewhere between 106 to 162 gallons of alcohol before Jesus provided more! This is far more than enough to make the most casual drinker drunk.
If Jesus provided alcohol to those who had already consumed over 100 gallons of alcohol, he both aided and encouraged their drunkenness, which would make him a sinner. Consider what Habakkuk wrote by inspiration, Habakkuk 2:15 (KJV) 15 Woe unto him that giveth his neighbour drink, that puttest thy bottle to him, and makest him drunken also, that thou mayest look on their nakedness! The sin Habakkuk is rebuking is the sin of contributing to drunkenness. However, we know Jesus was without sin (1 Pet 2:22), so that he could be the propitiation (sin offering) for us (1 John 4:10). Jesus knew what was recorded by Solomon when he wrote by inspiration, "Wine is a mocker, strong drink is raging: and whosoever is deceived thereby is not wise" (Proverbs 20:1).
The common daily drink of grape juice (οινου) was often made from a concentrate (paste) which was preserved in wine skins to keep it from fermenting. This paste was mixed into the waterpots, much like we mix kool-aid to give the water flavoring. There was fermented wine also, which was produced for the purpose of intoxication. We have many verses condemning the drinking of this fermented alcohol. In Titus 2:3 and 1 Tim. 3:8 we see the phrase “not given to much wine”. The phrase “to much” can be translated “in any respect”, thus resulting in the understanding of “not given in any respect to wine”. This agrees with Eph 5:18 (KJV) 18 And be not drunk with wine, wherein is excess; but be filled with the Spirit;. The word “drunk” is “μεθυσκεσθε” which is describing the process of becoming intoxicated and not the end result of drunkenness. Thus, Jesus could not aid in the process of their becoming intoxicated by providing Alcoholic beverage. Why? Because science has confirmed what the Bible has continuously warned; one starts to become intoxicated with the very first drink of alcoholic beverage. With close examination, we must conclude that the Lord did not make intoxicating wine at the marriage feast in Cana of Galilee.