In 1 Timothy, chapter 3 Paul speaks to Timothy about qualifications for overseers and deacons, ie men who are active serving in the church. It seems obvious that this is an ideal that applies to everyone, as we are all called to be active in the church. This is quoted from New International Version
1"Here is a trustworthy saying,: If anyone sets his heart on being an overseer, he desires a noble task. 2 Now the overseer must be above reproach, the husband of but one wife, temperate, self-controlled, respectable, hospitable, able to teach, 3 not given to drunkenness, not violent but gentle, not quarrelsome, not a lover of money. 4 He must manage his own family well and see that his children obey him with proper respect. 5 (If anyone does not know how to manage his own family, how can he take care of God's church?)"
and then in verse 11 (speaking of deacons which are simply those who serve)
"In the same way their wives are to be women worthy of respect, not malicious talkers but temperate and trustworthy in everything. 12 A deacon must be the husband of but one wife and must manage his children and his household well."
Now that says the man is to "manage" his household well. Why would anyone say that he is not the head of the household? The buck stops at him, and with that comes a huge degree of responsibility. Notice as well in Genesis 3:16, Eve's curse is, "Your desire will be for your husband, and he will rule over you." The Hebrew word for husband actually means our desire will be for his role, his authority. So, it can't be Biblical to say that the wife is in charge of the household and makes the decisions, and the man just has to provide, if even that. That is not falling under the authority God has ordered for us, (as women), and though it can be difficult at times, if we seek the Spirit's transforming power and guidance, this is the way things will go smoothest and most rewarded by our Father.
If the Bible says an overseer must manage his own family well, then he should do that. If the Bible says the husband is the head of the wife like Christ is head of the church, then he should do that.
The problem is an issue of accuracy - when people quote "head of household," they are confusing two concepts, "head of the wife" and "household" (so far a word not quoted in either of the verses we've mentioned). It's important to get this right because the concept is more than simply managing a household, it's about managing a family (relationship), and being a head of wife (relationship) like Christ is head of the church (relationship). The difference is that when you reduce it to "household," you drain the parallel in Eph. 5 of meaning because Christ did not die for his bride, his church, so that he could simply be in charge. It was about reconciling children with their father, it was about family, and love.
I'm just saying "head of household" is reductionist, and leaving out the heart (no pun intended) of the message.
My husband and I read a great book by Dr. Sarah Sumner, called, "Men and Women in the Church."
One of the most important things I got out of her book is the understanding that what the Bible says, goes. And what the Bible says is not what most people quote.
"the husband is the head of the wife as Christ is the head of the church"
The Bible simply does NOT say that the husband is the head of the household, and to change his role from being the head of the wife to the head of the household is not only to reduce his job, but to disconnect him from the wife - his body, in the same way the church is Christ's body.
There's a whole chapter on this verse and the implications of this wording so I won't go into it all (I do recommend the book, though). But what I would like to say is that being the head of a person (wife) - like Christ is the head of the church (not the building or the organization, but the very believers themselves), has really helped me understand how husband and wife are to be like the church and Christ - serving and loving each other.