Authority 7: one another

In his letter Grudem remarks that "one another" in "submit to one another" means that some submit to others. Grudem writes,

My argument for Ephesians 5:21 is that "being subject" to someone in the sense intended by Greek hypotassō is a one-directional activity. In that sense it is like the action of "killing one another" - in the nature of the action of killing, one person kills and the other is killed. The dead person does not rise from the dead after a few minutes and kill the other person, nor could every single person kill every single other person. Killing one another rather has the sense "some to others," in that some were killing others.

I thought I would do a rough search in English for "one another" in the scriptures. I found the following,

discuss with one another
say to one another
ask one another
trample one another
accept glory from one another
stare at one another
love one another
degrading their bodies with one another
inflamed with lust for one another
devoted to one another
honor one another
livein harmony with one another
pass judgement on one another
accept one another
instruct one another
greet one another
agree with one another
encourage one another
serve one another
bear with one another
be kind and compassionate with one another
speak to another with psalms, etc.
submit to one another
in your relationships with one another, have the same attitude of mind Christ Jesus had
forgive one another
admonish one another
hate one another
spur one another on to love
do not slander one another
don't grumble against one another
offer hospitality to one another
clothe yourselves with humility toward one another
have fellowship with one another
lay down our lives for one another

I do not see one instance in which one class of person is to follow these commands towards another class of person. I do not believe that Christians are broken into two classes, male and female, and female are to submit to male, and male are to have authority over female. That is the implication of the interpretation that some Christians are to submit to other Christians.Quite frankly, I don't see how Christianity would be a revolutionary religion if that were the case.

The teaching to serve and offer hospitality to one another is surely that one person offers hospitality to another and later in return, the other offers hospitality. Each offers hospitality and service out of their ability to do so.