I think Christ chose to let this be His first miracle to show His support for the institution of marriage and how it points to that between Himself and the Church, and also because of the temporal blessing and joy that marriage is.
My study Bible comments on John 2:3: “the wedding party’s running out of wine may be seen as symbolizing the spiritual barrenness of first-century Judaism, especially against an OT background that viewed wine (but never drunkenness) as a sign of joy and God’s blessing (Ps. 104:15; Prov. 3:10; cf Matt 26: 29).”
Wine is a gift from God. Pomegranate wine, in my opinion, is a greater gift. ; )
The pomegranate: A Rosh Hashanah symbol (includes pomegranate recipes and this statement: “In the sensual poetry of Song of Songs, we read: … ‘I would cause thee to drink of spiced wine, of the juice of my pomegranate’ (Song of Songs 8:2).”