I'm going to make the assumption that red wine is an acquired taste for nearly everyone. Perhaps that is a symbol. Keeping God's commandments is offensive when first attempting it, but it becomes an acquired taste. It begins to become delicious to the soul.

Casual drinking of wine is advised against in the Word of Wisdom.1 Perhaps this "profane" use is a mockery of the purpose to which it has been ordained because it dilutes this symbolism.
 

In the two instances demonstrated in the Book of Mormon of the Savior giving the sacrament,2 the disciples ate first, then the disciples gave to the multitude. In other words the disciples symbolically had to have taken the bread of life within themselves, before they could be enabled to impart to anyone else. It is easy to take offense at this symbolism, as some partake first, while all else (including all women) wait, but there needn't be any.

Men and women are can be viewed as veil workers. The woman works the veil by bringing souls into the mortal world. The man works the veil by bringing souls into the eternal world. When the woman has the baby, the man does not much except to watch and help support in the difficulty occurring. When the man is attempting to part the veil, likewise a long process of travail occurs, but the woman plays more of a supportive role, as did the man at the beginning.

In the Millennial-like circumstance, even if it is just within one family, this can be reversed. Because as the man has been brought into the world by the woman, woman is brought into the eternal world of the man. Both roles have been fulfilled as a chiasm, both now have a priesthood.

It is in this role that men have nearly universally failed, while, in their role, women almost never have.

I gave a credit of the second idea (about veil workers) to LHB (which she brought up during our sacrament) because that is where credit belongs, but she said no, because I fleshed out the details. She had wisdom or a natural intuitive process, but I filled in the details with knowledge. The example in Adam and Eve is that Eve responds to the prophecy of Adam with wisdom. Perhaps the reverse is also typical, where wisdom intuits, and knowledge fills in.

This led to another discussion of Adam and Eve in the Garden.

Denver suggests that Adam and Eve partook of the fruit before the appointed time, and had they waited for the Sabbath to be observed, they would have entered in a state not unlike the millennium.3 This doesn't void the responsibility of their children, however. We each partake of the tree and are cast out of the garden, thus they individually would have (and currently do) chose to abide a Terrestrial or Telestial law.

 

Notes

1. "That inasmuch as any man drinketh wine or strong drink among you, behold it is not good, neither meet in the sight of your Father, only in assembling yourselves together to offer up your sacraments before him. And, behold, this should be wine, yea, pure wine of the grape of the vine, of your own make." (D&C 89:5-6)

2. 3 Nephi 18, 20.

3. Adam and Eve.