The discussion over at dotCommonweal reveals at attitude toward marriage that it is private affair which the couple should be able to celebrate in their own way.
In the Western Church, following Roman law, the essence of marriage is considered the mutual consent of the spouses. The priest is only a witness, and his presence was not even required until after the Council of Trent. In the Eastern Church, however, the priest is the minister of marriage. The couple does not marry themselves: the Church, through the priest, marries them.
There are strong traces of this even in the Reformed Churches. As the Prayer Book has it:
Dearly beloved, we are gathered together here in the sight of God, and in the face of this company, to join together this Man and this Woman in holy Matrimony…
The Catholic Church in the West, although it considerers the couple the ministers of the marriage, insists that if at all possible the marriage be performed in a church. Everyone seems to consider it a “private” wedding, but of course anyone can attend. At my wedding in St. Matthew’s Cathedral in Washington we had a bag lady (whom I had gotten to know) and a few bums at the mass, and probably some tourists as well.
Standing before the assembled crowd and making my vows in the presence of the Holy Trinity made me take the whole affair very, very seriously.
We also used the Prayer Book form of the vows, and the beautiful words With this ring I thee wed, in the name of the Father, and of the Son, and of the Holy Ghost.
Apparently some couples get married at a parish mass; this is an excellent idea, and it would end a lot of nonsense. It would also stress the marriage as an act not only of the couple but of the entire community.