Many of the answers focus on patriarchy in the marriage. To me that is the correct response even though you asked about society as well.
One of the reasons the Jews rejected the Gospel was because the Messiah did not establish an earthly kingdom as they expected. I don't think we are called to establish a theocratic state where all citizens must obey christian beliefs at the end of a gun. Jesus wants to be chosen, not forced upon people.
With that in mind, I don't think a patriarchal society is necessarily a christian goal. The goal is to conduct our homes and congregations the way God designed. The more Christianity grows, the more the society will look patriarchal simply because more people will be living as God designed. In my blog post on gender roles, I used the example of a wife voting differently from her husband as an example of sinful rebellion. I am not claiming women should not be allowed to vote, I am claiming her vote should double the voting power of her husband. In doing so, she is an asset to her husband's mission, not a hindrance.
Earthly patriarchy usually describes a tyranny where women are subjugated by force in some way. Biblical Patriarchy is the Husband/Father leading the family as a reflection of Christ and a wife/daughter willingly submitting to her husband/father. It also includes following the biblical structure of the local congregation with men as elders.
Read the following guidelines for gender roles and ask yourself if biblical patriarchy is deserving of the negative emotions that are linked to it?
Biblical guidelines for how men should act:
- Love your wife as Christ loves the church
- Be sober-minded,
- Be dignified,
- Be self-controlled,
- Be sound in faith,
- Be sound in love,
- Be sound in steadfastness
- Be a model of good works,
- In your teaching show integrity, dignity, and sound speech
- Live with your wife in an understanding way
- Show your wife honor as a fellow heir of the grace of life
- Do not be embittered against your wife
- Do not provoke your children
- Bring children up in the discipline and instruction of the Lord
Biblical guidelines for how women should act:
- Embrace your purpose as a helper to your husband
- Have children
- Revere your husband the way the church reveres Christ
- Submit to your husband’s rule. If unmarried, submit to your father’s rule.
- Have a gentle and quiet spirit
- Be silent in church and receive instruction with submissiveness
- Teach younger women to love their husbands, to love their children, to be sensible, pure, workers at home, kind, being subject to their own husbands
- Don’t gossip
- The home should be your priority. A husband may need you to work outside the home, but the goal should be the wife care for the children and the home.