A woman asked John Piper if it was okay for women to become police officers. He answered her here. I will give a few comments from his article and then respond.
“And here’s my conviction: to the degree that a woman’s influence over a man — guidance of man, leadership of man — is personal and directive, it will generally offend a man’s good, God-given sense of responsibility and leadership, and thus controvert God’s created order. To an extent, a woman’s leadership or influence may be personal and non-directive, or directive and non-personal. I don’t think those would necessarily push the limits of what is appropriate.
“That’s my general paradigm of guidance, and you can see how flexible it is, how imprecise it is, so let me give some examples. A woman who is a civil engineer might design a traffic pattern in a city so that she’s deciding which streets are one-way, and therefore she is influencing, indeed controlling in one sense, all the male drivers all day long. But this influence is so non-personal that it seems to me that the feminine/masculine dynamic is utterly negligible in this kind of relationship.
“On the other hand, a husband and wife relationship is very personal, and hence the clear teaching of the New Testament that the man should give leadership in the home, and that she should give glad partnership in supporting and helping that leadership come into its own.
“On the other hand, some influence is very directive, and some is non-directive. For example, a drill sergeant might epitomize directive influence over the privates in the platoon, and it would be hard for me to see how a woman could be a drill sergeant — ‘hut two, right face, left face, keep your mouth shut, private’ — over men without violating their sense of manhood and her sense of womanhood.”