Dr. Joel Beeke explains in this video that the word "patriarchy" can be interpreted wrongly. It could involve a degradation of women and children because the father is harsh and authoritarian. There is a difference. It is important to understand that the husband and the wife are parents together. The father must teach his children to have great respect for their mother. Both should work together as a team with the husband ultimately being able to make the final call, but the husband should do this lovingly.
1 Peter 3:7 (NKJV) - "Husbands, likewise, dwell with them with understanding, giving honor to the wife, as to the weaker vessel, and as being heirs together of the grace of life, that your prayers may not be hindered."
The Patriarchy actually means the rule of the Father, literally. And there's a very biblical concept to that. The father is the head of the home and is commanded to be so. That's an imperative in Ephesians 5. Jesus makes it plain too that the husband is the head of the wife.
But unbiblical patriarchy is when the man rules the family as a kind of sufficient be-all and end-all himself. And then patriarchy is taken on kind of a negative connotation of degrading women and degrading children because the father can have a kind of a harsh authoritarianism. So there's a difference between exercising biblical authority and falling into the quagmire of authoritarianism. I think that it's important to understand that the husband and the wife are parents together over the children and the father must teach the children to have deep great respect for the mother and not treat the mother like another child and contradict her and that type of thing. In the parental role husband and wife should work together as a team.
But of course, there is one head of a home so that when sometimes when final decisions need to be made, the wife needs to say to the husband, We've discussed this together and now I trust your judgment. If there's say some disagreement on a non sinful issue and I'll leave the final decision up to you. But it's a very loving headship. You