There is something which a lot of people don't seem to understand: there is no authority without responsibility. The captain of the ship is also responsible for everything happening on board the ship. The one taking a decision is ultimately responsible for the consequences of this decision. Parents have authority over their minor children because they are financially and otherwise responsible for the children and their behaviour.
In the same manner, the husband can't truly be the head of the family if his wife is a co-breadwinner. He can't demand she obey him when she fully shares in the responsibility to provide, or even worse, when he stays home and she goes out to work. Oh she can humour him and treat him as one but it won't be anything more than LARPing.
Being the breadwinner gives a person a certain power, economic power, that's why feminists hate traditional family so much. It makes the woman a dependent. Any person who claims to be pro-traditional family and pro-male headship but expects and encourages married women to work is either very dishonest or very stupid or both.
As a man, you can't expect your wife to be an empowered career woman by day and then come home, change into a sexy outfit and become a little submissive Suzy Homemaker. You can't expect her to work the same amount of hours as yourself and then do all the housework. She can't be there for your children and at the office at the same time. And after long working hours she will be tired and less interested in sex, too.
At my blog, I'm trying to support traditional families and I'm generally operating on the principle that those who aren't against us are with us, but I'm getting quite suspicious of anyone who promotes male authority without stressing male responsibility. No taxation without representation, no authority without responsibility.