Why do Christians drink wine at the Lord's Supper but at no other time?

Am I right in refusing to take the cup at the Lord’s Table because it is not “non-alcoholic”?

That the wine used by the Lord at the institution of the Lord’s Supper was the ordinary wine of the country, nothing but special pleading can deny. The vintage was then long past, so that any idea of fresh grape juice and water is ruled out. At Corinth (see 1 Corinthians 11: ), the erroneous idea had crept in that the Lord’s Supper was to be a meal, and each brought his or her provisions, and “one was hungry and another drunken”! How does the apostle meet this scandal? Not by advocating the use of some substitute for the ordinary wine used, but by showing that it was not a meal, but a memorial act, for which a morsel of bread or a sup of wine sufficed. I am not advocating the habitual use of wine as a beverage; on the contrary, but for anyone to refuse to partake of the cup, which the Lord Himself instituted, because it contains wine, which some have abused, seems like setting up himself to be wiser than God, and to incur a serious responsibility.