The theology of the traditional wedding service is based on Ephesians 5, as Peter Ould has explained in his analysis of the gay wedding liturgy used used May 31st in London on May 31st.
The traditional service teaches that "Marriage signifies unto us the mystical union that is betwixt Christ and his church." Ephesians 5 makes this connection in the context of discussing the roles of husband and wife. The husband is to love the wife as Christ loves the church and the wife is to obey the husband as the Church obeys Christ.
22Wives, submit to your husbands as to the Lord. 23For the husband is the head of the wife as Christ is the head of the church, his body, of which he is the Savior. 24Now as the church submits to Christ, so also wives should submit to their husbands in everything.In the traditional service between man and woman, the wife makes the vow to obey the husband and the husband makes the vow to love the wife. We are taught a theology of obedience to Christ as we participate in the liturgy.
25Husbands, love your wives, just as Christ loved the church and gave himself up for her 26to make her holy, cleansing[b] her by the washing with water through the word, 27and to present her to himself as a radiant church, without stain or wrinkle or any other blemish, but holy and blameless. 28In this same way, husbands ought to love their wives as their own bodies. He who loves his wife loves himself. 29After all, no one ever hated his own body, but he feeds and cares for it, just as Christ does the church— 30for we are members of his body. 31"For this reason a man will leave his father and mother and be united to his wife, and the two will become one flesh."[c] 32This is a profound mystery—but I am talking about Christ and the church. 33However, each one of you also must love his wife as he loves himself, and the wife must respect her husband.
In the new wedding liturgy for the gay couple in London, we are taught that their union also symbolizes the mystical union of Christ and his Church:"Such a covenant shows us the mystery of the union between God and his people and Christ and his Church." However, in this service, neither of the men make a vow of obedience to the other. Both make the same vow to love, honor and keep. Neither is clearly representing Christ and neither is clearly representing the Church and there is no separate vow that would represent the commitment of Christ to his Church differentiated from the commitment of the Church to obey Christ.
Thus the new theology of equality with Christ is embedded in the new wedding liturgy. We are not called to obey Christ. We are called to loving fellowship with Christ but obedience is not required.